Partial differential equations, spectral theory, and mathematical physics: the Ari Laptev anniversary volume
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| Other Authors: | , , , , |
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| Format: | Book |
| Language: | English |
| Published: |
Berlin, Germany
EMS Press
[2021]
|
| Series: | EMS series of congress reports
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | xii, 481 Seiten Illustrationen, Diagramme 25 cm |
| ISBN: | 9783985470075 3985470073 |
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| 020 | |a 3985470073 |c Festeinband |9 3-98547-007-3 | ||
| 024 | 3 | |a 9783985470075 | |
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| 084 | |a 510 |2 23sdnb | ||
| 084 | |a 530 |2 23sdnb | ||
| 245 | 1 | 0 | |a Partial differential equations, spectral theory, and mathematical physics |b the Ari Laptev anniversary volume |c edited by Pavel Exner, Rupert L. Frank, Fritz Gesztesy, Helge Holden, Timo Weidl |
| 264 | 1 | |a Berlin, Germany |b EMS Press |c [2021] | |
| 264 | 4 | |c © 2021 | |
| 300 | |a xii, 481 Seiten |b Illustrationen, Diagramme |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a EMS series of congress reports | |
| 653 | |a heat kernel estimates | ||
| 653 | |a nonlinear Schrödinger equation | ||
| 653 | |a Lieb–Thirring inequality | ||
| 653 | |a Bogoliubov theory | ||
| 653 | |a Wehrl-type entropy inequalities | ||
| 653 | |a Euler–Bardina equations | ||
| 653 | |a d-bar problem | ||
| 653 | |a Friedrichs inequality | ||
| 653 | |a Bose–Einstein condensation | ||
| 653 | |a wave packet evolution | ||
| 653 | |a electron density estimates | ||
| 653 | |a Brezis–Nirenberg problem | ||
| 653 | |a Feshbach–Schur map | ||
| 653 | |a stability of matter | ||
| 653 | |a scattering theory | ||
| 653 | |a Hardy inequality | ||
| 655 | 7 | |0 (DE-588)4016928-5 |a Festschrift |2 gnd-content | |
| 655 | 7 | |0 (DE-588)4143413-4 |a Aufsatzsammlung |2 gnd-content | |
| 700 | 1 | |a Laptev, Ari |d 1950- |0 (DE-588)1012993876 |4 hnr | |
| 700 | 1 | |a Exner, Pavel |d 1946- |0 (DE-588)134284410 |4 edt | |
| 700 | 1 | |a Frank, Rupert L. |d 1978- |0 (DE-588)1236600002 |4 edt | |
| 700 | 1 | |a Gesztesy, Fritz |d 1953- |0 (DE-588)134200136 |4 edt | |
| 700 | 1 | |a Holden, Helge |d 1956- |0 (DE-588)111693667 |4 edt | |
| 700 | 1 | |a Weidl, Timo |d ca. 20./21. Jh. |0 (DE-588)1095129147 |4 edt | |
| 710 | 2 | |a European Mathematical Society Publishing House ETH-Zentrum SEW A27 |0 (DE-588)1066118477 |4 pbl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-9854750-7-0 |w (DE-604)BV047306383 |
| 856 | 4 | 2 | |m B:DE-101 |q application/pdf |u https://d-nb.info/1233748750/04 |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032899712&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-032899712 | ||
Record in the Search Index
| _version_ | 1804182829068713984 |
|---|---|
| adam_text | CONTENTS
PREFACE
....................................................................................................................
V
1
A
NON-EXISTENCE
RESULT FOR
A
GENERALIZED
RADIAL
BREZIS-NIRENBERG
PROBLEM
..............................................................................................................
1
BY
RAFAEL
D.
BENGURIA
AND
SOLEDAD
BENGURIA
1
INTRODUCTION
..............................................................................................
1
2
NON-EXISTENCE
OF
SOLUTIONS,
VIA
THE
POHOZAEV
VIRIAL
IDENTITY,
USING
THE
CONFORMAL
LAPLACIAN
..............................................................................
5
3
NON-EXISTENCE
OF
SOLUTIONS
USING
THE
RELLICH-POHOZAEV
ARGUMENT
AND
A
HARDY-TYPE
INEQUALITY
........................................................................
9
4
AN
ILLUSTRATIVE
EXAMPLE
...........................................................................
12
BIBLIOGRAPHY
....................................................................................................
14
2
FRIEDRICHS-TYPE
INEQUALITIES
IN
ARBITRARY
DOMAINS
......................................
17
BY
ANDREA
CIANCHI
AND
VLADIMIR
MAZYA
1
INTRODUCTION
..............................................................................................
17
2
BACKGROUND
AND
NOTATIONS
.........................................................................20
3
FIRST-ORDER
INEQUALITIES
...............................................................................
23
4
SECOND-ORDER
INEQUALITIES
............................................................................
27
5
INEQUALITIES
FOR
THE
SYMMETRIC
GRADIENT
......................................................
33
6
SKETCHES
OF
PROOFS
.........................................................................................34
BIBLIOGRAPHY
.........................................................................................................
37
3
ARI
LAPTEV
AND
THE
JOURNAL
OF
SPECTRAL
THEORY
.............................................
39
BY
E.
BRIAN
DAVIES
4
CRITICAL
MAGNETIC
FIELD
FOR
2D
MAGNETIC
DIRAC-COULOMB
OPERATORS
AND
HARDY
INEQUALITIES
...............................................................................................
41
BY
JEAN
DOLBEAULT,
MARIA
J.
ESTEBAN
AND
MICHAEL
LOSS
1
INTRODUCTION
AND
MAIN
RESULTS
......................................................................
41
2
HOMOGENEOUS
HARDY-LIKE
INEQUALITIES
......................................................
49
3
THE
MINIMIZATION
PROBLEM
.........................................................................
50
4
THE
2D
MAGNETIC
DIRAC-COULOMB
OPERATOR
WITH
AN
AHARONOV-BOHM
MAGNETIC
FIELD
...............................................................................................
53
5
NON-RELATIVISTIC
LIMIT
..................................................................................
56
A
APPENDIX
......................................................................................................
57
BIBLIOGRAPHY
........................................................................................................
60
VIII
CONTENTS
5
THE
FESHBACH-SCHUR
MAP
AND
PERTURBATION
THEORY
....................................
65
BY
GENEVIEVE
DUSSON,
ISRAEL
MICHAEL SIGAL
AND
BENJAMIN
STAMM
1
SET-UP
AND
RESULT
.........................................................................................
65
2
PERTURBATION
ESTIMATES
............................................................................
70
3
APPLICATION:
THE
GROUND
STATE
ENERGY
OF
THE
HELIUM-TYPE
IONS
....
76
A
THE
EIGENFUNCTIONS
OF
THE
HYDROGEN-LIKE
HAMILTONIAN
.......................
84
B
THE
NUMERICAL
APPROXIMATION
OF
THE
CONSTANTS
WI,
U 2,
WF
S
AND
WF
.
.
84
BIBLIOGRAPHY
.........................................................................................................
87
6
ADIABATIC
AND
NON-ADIABATIC
EVOLUTION
OF
WAVE
PACKETS
AND
APPLICATIONS
TO
INITIAL
VALUE
REPRESENTATIONS
..........................................................................
89
BY
CLOTILDE
FERMANIAN
KAMMERER,
CAROLINE
LASSER
AND
DIDIER
ROBERT
1
INTRODUCTION
...................................................................................................
89
2
PROPAGATION
OF
GAUSSIAN
STATES
AND
THE
HERMAN-KLUK
APPROXIMATION
FOR
SCALAR
EQUATIONS
......................................................................................92
3
HERMAN-KLUK
FORMULA
IN
THE
ADIABATIC
SETTING
..........................................
94
4
WHAT
ABOUT
SMOOTH
CROSSINGS?
...................................................................
98
5
A
SKETCHY
PROOF
FOR
HERMAN-KLUK
APPROXIMATIONS
...............................
102
BIBLIOGRAPHY
.......................................................................................................
ILL
7
LENGTH
SCALES
FOR
BEC
IN
THE
DILUTE
BOSE
GAS
...............................................
115
BY
S0REN
FOUMAIS
1
INTRODUCTION
.................................................................................................
115
2
ENERGY
IN
SMALL
BOXES
.................................................................................
119
3
LOCALIZATION
TO
SMALL
BOXES
........................................................................
127
A
FACTS
ABOUT
THE
SCATTERING
SOLUTION
............................................................
132
BIBLIOGRAPHY
.......................................................................................................
132
8
THE
PERIODIC
LIEB-THIRRING
INEQUALITY
...........................................................
135
BY
RUPERT
L.
FRANK,
DAVID
GONTIER
AND
MATHIEU
LEWIN
1
THE
PERIODIC
LIEB-THIRRING
INEQUALITY
.....................................................
135
2
THE
ONE-DIMENSIONAL
INTEGRABLE
CASE
Y
=
|
...........................................
140
3
NUMERICAL
SIMULATIONS
IN
ID
AND
2D
........................................................
143
A
A
MINIMIZATION
PROBLEM
WITH
ENTROPY
......................................................
146
B
COMPUTATION
OF
THE
DENSITY
OF
STATES
OF
...............................................
147
BIBLIOGRAPHY
.......................................................................................................
153
9
SEMICLASSICAL
ASYMPTOTICS
FOR
A
CLASS
OF
SINGULAR
SCHRODINGER
OPERATORS
........................................................................................
155
BY
RUPERT
L,
FRANK
AND
SIMON
LARSON
1
INTRODUCTION
.................................................................................................
155
2
PRELIMINARIES
..............................................................................................
157
3
LOCAL
ASYMPTOTICS
........................................................................................
161
CONTENTS
IX
4
FROM
LOCAL
TO
GLOBAL
ASYMPTOTICS
..............................................................
170
A
PROPERTIES
OF
P
V
..........................................................................................
172
BIBLIOGRAPHY
.......................................................................................................
175
10
ON
THE
SPECTRAL
PROPERTIES
OF
THE
BLOCH-TORREY
EQUATION
IN
INFINITE
PERIODICALLY
PERFORATED
DOMAINS
....................................................................
177
BY
DENIS
S,
GREBENKOV,
BERNARD
HELFFER
AND
NICOLAS
MOUTAL
1
INTRODUCTION
.................................................................................................
177
2
THE
BLOCH-TORREY
OPERATOR
IN
THE
PERFORATED
WHOLE
PLANE
......................
178
3
FLOQUET
APPROACH
FOR
Y
-PERIODIC
PROBLEMS
..............................................
179
4
THE
BLOCH-TORREY
OPERATOR
IN
A
PERFORATED
CYLINDER
CONTINUED
..............
184
5
QUASI-MODES
AND
NON-EMPTINESS
OF
THE
SPECTRUM
............................
190
6
CONCLUSION
.................................................................................................
192
A
GENERALIZED
LAX-MILGRAM
THEOREM
............................................................
193
B
SPECTRUM
AND
WEYL
S
SEQUENCES
...............................................................
194
BIBLIOGRAPHY
.......................................................................................................
195
11
COUNTING
BOUND
STATES
WITH
MAXIMAL
FOURIER
MULTIPLIERS
........................
197
BY
DIRK
HUNDERTMARK,
PEER
KUNSTMANN,
TOBIAS
RIED
AND
SEMJON
VUGALTER
1
INTRODUCTION
.................................................................................................
197
2
THE
SPLITTING
TRICK
.......................................................................................
201
BIBLIOGRAPHY
.......................................................................................................
206
12
SHARP
DIMENSION
ESTIMATES
OF
THE
ATTRACTOR
OF
THE
DAMPED
2D
EULER-BARDINA
EQUATIONS
...........................................................................
209
BY
ALEXEI
ILYIN
AND
SERGEY
ZELIK
1
INTRODUCTION
................................................................................................
209
2
GLOBAL
ATTRACTOR
..........................................................................................
212
3
DIMENSION
ESTIMATE
....................................................................................
214
4
A
SHARP
LOWER
BOUND
................................................................................
216
5
APPENDIX
...................................................................................................
222
BIBLIOGRAPHY
.......................................................................................................227
13
UPPER
ESTIMATES
FOR
THE
ELECTRONIC
DENSITY
IN
HEAVY
ATOMS
AND
MOLECULES
.............................................................................................................
231
BY
VICTOR
IVRII
1
INTRODUCTION
................................................................................................
231
2
MAIN
INTERMEDIATE
INEQUALITY
....................................................................
233
3
ESTIMATES
OF
THE
AVERAGED
ELECTRONIC
DENSITY
...........................................
236
4
ESTIMATES
OF
THE
CORRELATION
FUNCTION
.......................................................
238
5
PROOF
OF
THEOREM
1.1
.................................................................................
242
BIBLIOGRAPHY
.......................................................................................................
245
X
CONTENTS
14
NON-LINEAR
SCHRODINGER
EQUATION
IN
A
UNIFORM
MAGNETIC
FIELD
................
247
BY
THOMAS
F.
KIEFFER
AND
MICHAEL
LOSS
1
INTRODUCTION
.................................................................................................
247
2
NON-LINEAR
MAGNETIC
SCHRODINGER
EQUATION
..............................................
249
3
THE
NON-LINEAR
PAULI
EQUATION
....................................................................
260
BIBLIOGRAPHY
.......................................................................................................
264
15
LARGE
|FC|
BEHAVIOR
OF
D-BAR
PROBLEMS
FOR
DOMAINS
WITH
A
SMOOTH
BOUNDARY
.............................................................................................................
267
BY
CHRISTIAN
KLEIN,
JOHANNES
SJOSTRAND
AND
NIKOLA
STOILOV
1
INTRODUCTION
.................................................................................................
267
2
MAIN
RESULT
.................................................................................................
269
BIBLIOGRAPHY
.......................................................................................................
275
16
HEAT
KERNEL
ESTIMATES
FOR
TWO-DIMENSIONAL
RELATIVISTIC
HAMILTONIANS
WITH
MAGNETIC
FIELD
..............................................................................................
277
BY
HYNEK
KOVARIK
1
INTRODUCTION
.................................................................................................
277
2
RADIAL
MAGNETIC
FIELD
.................................................................................
278
3
AHARONOV-BOHM-TYPE
MAGNETIC
FIELDS
....................................................
283
BIBLIOGRAPHY
.......................................................................................................288
17
A
VERSION
OF
WATSON
LEMMA
FOR
LAPLACE
INTEGRALS
AND
SOME
APPLICATIONS
..........................................................................................................
289
BY
STANISLAS
KUPIN
AND
SERGEY
NABOKO^
1
INTRODUCTION
.................................................................................................289
2
PROOFS
OF
THE
RESULTS
....................................................................................
293
3
SOME
COROLLARIES
.......................................................................................297
BIBLIOGRAPHY
.......................................................................................................
300
18
WEHRL-TYPE
COHERENT
STATE
ENTROPY
INEQUALITIES
FOR
SU(1,
1)
AND
ITS
AX
4
B
SUBGROUP
..............................................................................................
301
BY
ELLIOTT
FL
LIEB
AND
JAN
PHILIP
SOLOVEJ
1
INTRODUCTION
.............................................................................................
301
2
UNITARY
REPRESENTATIONS
AND
COHERENT
STATES
FOR
THE
AX
4
B
GROUP
.
.
304
3
GENERALIZED
CONJECTURE
FOR
THE
AX
+
B
GROUP
AND
A
PARTIAL
RESULT
.
.
305
4
AN
ANALYTIC
FORMULATION
..........................................................................308
5
SOME
UNITARY
SU(1,
1)
REPRESENTATIONS
AND
THEIR
COHERENT
STATES
.
.
.
.310
6
THE
SU(1,
1)
QUANTUM
CHANNELS
.........................................
312
BIBLIOGRAPHY
.......................................................................................................
312
CONTENTS
XI
19
BLOW-UPS
FOR
THE
HORN-KAPRANOV
PARAMETRIZATION
OF
THE
CLASSICAL
DISCRIMINANT
.......................................................................................................
315
BY
EVGENY
MIKHALKIN,
VITALY
STEPANENKO
AND
AVGUST
TSIKH
1
INTRODUCTION
................................................................................................
315
2
EXTREMAL
DISCRIMINANT
AND
FACTORIZATION
OF
ITS
TRUNCATIONS
.....................
318
3
PARAMETRIZATIONS
OF
ZERO
SETS
OF
DISCRIMINANTS
........................................322
4
BLOW-UPS
OF
HOM-KAPRANOV
PARAMETRIZATIONS
AND
PROOF
OF
THE
THEOREM
................................................................................................
324
BIBLIOGRAPHY
.......................................................................................................
328
20
EIGENVALUE
ESTIMATES
AND
ASYMPTOTICS
FOR
WEIGHTED
PSEUDODIFFERENTIAL
OPERATORS
WITH
SINGULAR
MEASURES
IN
THE
CRITICAL
CASE
................................
331
BY
GRIGORI
ROZENBLUM
AND
EUGENE
SHARGORODSKY
1
INTRODUCTION
................................................................................................
331
2
SETTING
AND
MAIN
RESULTS
.............................................................................
333
3
SOME
REDUCTIONS
..........................................................................................
337
4
GEOMETRY
CONSIDERATIONS
..........................................................................
341
5
ESTIMATES
...................................................................................................
344
6
APPROXIMATION
OF
THE
WEIGHT
....................................................................
350
7
THE
ASYMPTOTIC
FORMULA
.............................................................................
351
BIBLIOGRAPHY
.......................................................................................................
353
21
RELATIONS
BETWEEN
TWO
PARTS
OF
THE
SPECTRUM
OF
A
SCHRODINGER
OPERATOR
AND
OTHER
REMARKS
ON
THE
ABSOLUTE
CONTINUITY
OF
THE
SPECTRUM
IN
A
TYPICAL
CASE
.......................................................................................................
355
BY
OLEG
SAFRONOV
1
INTRODUCTION
................................................................................................
355
2
PROOF
OF
THEOREM
3.4
.................................................................................
363
BIBLIOGRAPHY
.......................................................................................................
364
22
BOGOLIUBOV
THEORY
FOR
MANY-BODY
QUANTUM
SYSTEMS
..................................
367
BY
BENJAMIN
SCHLEIN
1
INTRODUCTION
................................................................................................
367
2
BOSE
GASES,
ENERGY
AND
DYNAMICS
..............................................................
368
3
THE
CORRELATION
ENERGY
OF
A
FERMI
GAS
....................................................
377
4
DYNAMICS
OF
A
FROHLICH
POLARON
..............................................................
382
BIBLIOGRAPHY
.......................................................................................................
386
23
A
STATISTICAL
THEORY
OF
HEAVY
ATOMS:
ASYMPTOTIC
BEHAVIOR
OF
THE ENERGY
AND
STABILITY
OF
MATTER
.......................................................................................
389
BY
HEINZ
SIEDENTOP
1
INTRODUCTION
................................................................................................389
2
BOUNDS
ON
THE
ENERGY
..............................................................................
392
XII
CONTENTS
3
STABILITY
OF
MATTER
.......................................................................................397
BIBLIOGRAPHY
.......................................................................................................
401
24
HOMOGENIZATION
OF
THE
HIGHER-ORDER
SCHRODINGER-TYPE
EQUATIONS
WITH
PERIODIC
COEFFICIENTS
..........................................................................................
405
BY
TATIANA
SUSLINA
1
INTRODUCTION
.................................................................................................
405
2
ABSTRACT
OPERATOR-THEORETIC
SCHEME
...........................................................
408
3
PERIODIC
DIFFERENTIAL
OPERATORS
IN
L2(^
D
;
C
N
)
........................................
412
4
APPLICATION
OF
THE
ABSTRACT
RESULTS
TO
A(K)
..............................................
415
5
APPROXIMATION
FOR
THE
OPERATOR
EXPONENTIAL
OF
A
.................................
421
6
HOMOGENIZATION
OF
THE
SCHRODINGER-TYPE
EQUATION
.................................
422
BIBLIOGRAPHY
.......................................................................................................
425
25
TRACE
FORMULAS
FOR
THE
MODIFIED
MATHIEU
EQUATION
.....................................
427
BY
LEON
A.
TAKHTAJAN
1
INTRODUCTION
.................................................................................................
427
2
GENERAL
CASE
.................................................................................................
430
3
EXAMPLES
....................................................................................................
434
4
EXISTENCE
OF
THE
SOLUTION
(X,
A)
...........................................................
440
BIBLIOGRAPHY
......................................................................................................
442
26
EIGENVALUE
ACCUMULATION
AND
BOUNDS
FOR
NON-SELFADJOINT
MATRIX
DIFFERENTIAL
OPERATORS
RELATED
TO
NLS
............................................................
445
BY
CHRISTIANE
TRETTER
1
INTRODUCTION
.................................................................................................
445
2
AUXILIARY
SPECTRAL
BOUNDS
OF
INDEPENDENT
INTEREST
.................................
447
3
INVARIANT
SUBSPACES
AND
NON-REAL
SPECTRUM
..............................................
450
BIBLIOGRAPHY
......................................................................................................
455
27
SCATTERING
THEORY
FOR
LAGUERRE
OPERATORS
...................................................
457
BY
DIMITRI
R.
YAFAEV
1
INTRODUCTION
.................................................................................................
457
2
JACOBI
OPERATORS
AND
ORTHOGONAL
POLYNOMIALS
........................................
460
3
WAVE
OPERATORS
..........................................................................................
462
4
TIME
EVOLUTION
..........................................................................................
468
BIBLIOGRAPHY
.......................................................................................................
478
LIST
OF
CONTRIBUTORS
.........................................................................
,
.....................
479
|
| adam_txt |
CONTENTS
PREFACE
.
V
1
A
NON-EXISTENCE
RESULT FOR
A
GENERALIZED
RADIAL
BREZIS-NIRENBERG
PROBLEM
.
1
BY
RAFAEL
D.
BENGURIA
AND
SOLEDAD
BENGURIA
1
INTRODUCTION
.
1
2
NON-EXISTENCE
OF
SOLUTIONS,
VIA
THE
POHOZAEV
VIRIAL
IDENTITY,
USING
THE
CONFORMAL
LAPLACIAN
.
5
3
NON-EXISTENCE
OF
SOLUTIONS
USING
THE
RELLICH-POHOZAEV
ARGUMENT
AND
A
"
HARDY-TYPE
"
INEQUALITY
.
9
4
AN
ILLUSTRATIVE
EXAMPLE
.
12
BIBLIOGRAPHY
.
14
2
FRIEDRICHS-TYPE
INEQUALITIES
IN
ARBITRARY
DOMAINS
.
17
BY
ANDREA
CIANCHI
AND
VLADIMIR
MAZYA
1
INTRODUCTION
.
17
2
BACKGROUND
AND
NOTATIONS
.20
3
FIRST-ORDER
INEQUALITIES
.
23
4
SECOND-ORDER
INEQUALITIES
.
27
5
INEQUALITIES
FOR
THE
SYMMETRIC
GRADIENT
.
33
6
SKETCHES
OF
PROOFS
.34
BIBLIOGRAPHY
.
37
3
ARI
LAPTEV
AND
THE
JOURNAL
OF
SPECTRAL
THEORY
.
39
BY
E.
BRIAN
DAVIES
4
CRITICAL
MAGNETIC
FIELD
FOR
2D
MAGNETIC
DIRAC-COULOMB
OPERATORS
AND
HARDY
INEQUALITIES
.
41
BY
JEAN
DOLBEAULT,
MARIA
J.
ESTEBAN
AND
MICHAEL
LOSS
1
INTRODUCTION
AND
MAIN
RESULTS
.
41
2
HOMOGENEOUS
HARDY-LIKE
INEQUALITIES
.
49
3
THE
MINIMIZATION
PROBLEM
.
50
4
THE
2D
MAGNETIC
DIRAC-COULOMB
OPERATOR
WITH
AN
AHARONOV-BOHM
MAGNETIC
FIELD
.
53
5
NON-RELATIVISTIC
LIMIT
.
56
A
APPENDIX
.
57
BIBLIOGRAPHY
.
60
VIII
CONTENTS
5
THE
FESHBACH-SCHUR
MAP
AND
PERTURBATION
THEORY
.
65
BY
GENEVIEVE
DUSSON,
ISRAEL
MICHAEL SIGAL
AND
BENJAMIN
STAMM
1
SET-UP
AND
RESULT
.
65
2
PERTURBATION
ESTIMATES
.
70
3
APPLICATION:
THE
GROUND
STATE
ENERGY
OF
THE
HELIUM-TYPE
IONS
.
76
A
THE
EIGENFUNCTIONS
OF
THE
HYDROGEN-LIKE
HAMILTONIAN
.
84
B
THE
NUMERICAL
APPROXIMATION
OF
THE
CONSTANTS
WI,
U 2,
WF
S
AND
WF
.
.
84
BIBLIOGRAPHY
.
87
6
ADIABATIC
AND
NON-ADIABATIC
EVOLUTION
OF
WAVE
PACKETS
AND
APPLICATIONS
TO
INITIAL
VALUE
REPRESENTATIONS
.
89
BY
CLOTILDE
FERMANIAN
KAMMERER,
CAROLINE
LASSER
AND
DIDIER
ROBERT
1
INTRODUCTION
.
89
2
PROPAGATION
OF
GAUSSIAN
STATES
AND
THE
HERMAN-KLUK
APPROXIMATION
FOR
SCALAR
EQUATIONS
.92
3
HERMAN-KLUK
FORMULA
IN
THE
ADIABATIC
SETTING
.
94
4
WHAT
ABOUT
SMOOTH
CROSSINGS?
.
98
5
A
SKETCHY
PROOF
FOR
HERMAN-KLUK
APPROXIMATIONS
.
102
BIBLIOGRAPHY
.
ILL
7
LENGTH
SCALES
FOR
BEC
IN
THE
DILUTE
BOSE
GAS
.
115
BY
S0REN
FOUMAIS
1
INTRODUCTION
.
115
2
ENERGY
IN
SMALL
BOXES
.
119
3
LOCALIZATION
TO
SMALL
BOXES
.
127
A
FACTS
ABOUT
THE
SCATTERING
SOLUTION
.
132
BIBLIOGRAPHY
.
132
8
THE
PERIODIC
LIEB-THIRRING
INEQUALITY
.
135
BY
RUPERT
L.
FRANK,
DAVID
GONTIER
AND
MATHIEU
LEWIN
1
THE
PERIODIC
LIEB-THIRRING
INEQUALITY
.
135
2
THE
ONE-DIMENSIONAL
INTEGRABLE
CASE
Y
=
|
.
140
3
NUMERICAL
SIMULATIONS
IN
ID
AND
2D
.
143
A
A
MINIMIZATION
PROBLEM
WITH
ENTROPY
.
146
B
COMPUTATION
OF
THE
DENSITY
OF
STATES
OF
.
147
BIBLIOGRAPHY
.
153
9
SEMICLASSICAL
ASYMPTOTICS
FOR
A
CLASS
OF
SINGULAR
SCHRODINGER
OPERATORS
.
155
BY
RUPERT
L,
FRANK
AND
SIMON
LARSON
1
INTRODUCTION
.
155
2
PRELIMINARIES
.
157
3
LOCAL
ASYMPTOTICS
.
161
CONTENTS
IX
4
FROM
LOCAL
TO
GLOBAL
ASYMPTOTICS
.
170
A
PROPERTIES
OF
P
V
.
172
BIBLIOGRAPHY
.
175
10
ON
THE
SPECTRAL
PROPERTIES
OF
THE
BLOCH-TORREY
EQUATION
IN
INFINITE
PERIODICALLY
PERFORATED
DOMAINS
.
177
BY
DENIS
S,
GREBENKOV,
BERNARD
HELFFER
AND
NICOLAS
MOUTAL
1
INTRODUCTION
.
177
2
THE
BLOCH-TORREY
OPERATOR
IN
THE
PERFORATED
WHOLE
PLANE
.
178
3
FLOQUET
APPROACH
FOR
Y
-PERIODIC
PROBLEMS
.
179
4
THE
BLOCH-TORREY
OPERATOR
IN
A
PERFORATED
CYLINDER
CONTINUED
.
184
5
QUASI-MODES
AND
NON-EMPTINESS
OF
THE
SPECTRUM
.
190
6
CONCLUSION
.
192
A
GENERALIZED
LAX-MILGRAM
THEOREM
.
193
B
SPECTRUM
AND
WEYL
'
S
SEQUENCES
.
194
BIBLIOGRAPHY
.
195
11
COUNTING
BOUND
STATES
WITH
MAXIMAL
FOURIER
MULTIPLIERS
.
197
BY
DIRK
HUNDERTMARK,
PEER
KUNSTMANN,
TOBIAS
RIED
AND
SEMJON
VUGALTER
1
INTRODUCTION
.
197
2
THE
SPLITTING
TRICK
.
201
BIBLIOGRAPHY
.
206
12
SHARP
DIMENSION
ESTIMATES
OF
THE
ATTRACTOR
OF
THE
DAMPED
2D
EULER-BARDINA
EQUATIONS
.
209
BY
ALEXEI
ILYIN
AND
SERGEY
ZELIK
1
INTRODUCTION
.
209
2
GLOBAL
ATTRACTOR
.
212
3
DIMENSION
ESTIMATE
.
214
4
A
SHARP
LOWER
BOUND
.
216
5
APPENDIX
.
222
BIBLIOGRAPHY
.227
13
UPPER
ESTIMATES
FOR
THE
ELECTRONIC
DENSITY
IN
HEAVY
ATOMS
AND
MOLECULES
.
231
BY
VICTOR
IVRII
1
INTRODUCTION
.
231
2
MAIN
INTERMEDIATE
INEQUALITY
.
233
3
ESTIMATES
OF
THE
AVERAGED
ELECTRONIC
DENSITY
.
236
4
ESTIMATES
OF
THE
CORRELATION
FUNCTION
.
238
5
PROOF
OF
THEOREM
1.1
.
242
BIBLIOGRAPHY
.
245
X
CONTENTS
14
NON-LINEAR
SCHRODINGER
EQUATION
IN
A
UNIFORM
MAGNETIC
FIELD
.
247
BY
THOMAS
F.
KIEFFER
AND
MICHAEL
LOSS
1
INTRODUCTION
.
247
2
NON-LINEAR
MAGNETIC
SCHRODINGER
EQUATION
.
249
3
THE
NON-LINEAR
PAULI
EQUATION
.
260
BIBLIOGRAPHY
.
264
15
LARGE
|FC|
BEHAVIOR
OF
D-BAR
PROBLEMS
FOR
DOMAINS
WITH
A
SMOOTH
BOUNDARY
.
267
BY
CHRISTIAN
KLEIN,
JOHANNES
SJOSTRAND
AND
NIKOLA
STOILOV
1
INTRODUCTION
.
267
2
MAIN
RESULT
.
269
BIBLIOGRAPHY
.
275
16
HEAT
KERNEL
ESTIMATES
FOR
TWO-DIMENSIONAL
RELATIVISTIC
HAMILTONIANS
WITH
MAGNETIC
FIELD
.
277
BY
HYNEK
KOVARIK
1
INTRODUCTION
.
277
2
RADIAL
MAGNETIC
FIELD
.
278
3
AHARONOV-BOHM-TYPE
MAGNETIC
FIELDS
.
283
BIBLIOGRAPHY
.288
17
A
VERSION
OF
WATSON
LEMMA
FOR
LAPLACE
INTEGRALS
AND
SOME
APPLICATIONS
.
289
BY
STANISLAS
KUPIN
AND
SERGEY
NABOKO^
1
INTRODUCTION
.289
2
PROOFS
OF
THE
RESULTS
.
293
3
SOME
COROLLARIES
.297
BIBLIOGRAPHY
.
300
18
WEHRL-TYPE
COHERENT
STATE
ENTROPY
INEQUALITIES
FOR
SU(1,
1)
AND
ITS
AX
4
B
SUBGROUP
.
301
BY
ELLIOTT
FL
LIEB
AND
JAN
PHILIP
SOLOVEJ
1
INTRODUCTION
.
301
2
UNITARY
REPRESENTATIONS
AND
COHERENT
STATES
FOR
THE
AX
4
B
GROUP
.
.
304
3
GENERALIZED
CONJECTURE
FOR
THE
AX
+
B
GROUP
AND
A
PARTIAL
RESULT
.
.
305
4
AN
ANALYTIC
FORMULATION
.308
5
SOME
UNITARY
SU(1,
1)
REPRESENTATIONS
AND
THEIR
COHERENT
STATES
.
.
.
.310
6
THE
SU(1,
1)
QUANTUM
CHANNELS
.
312
BIBLIOGRAPHY
.
312
CONTENTS
XI
19
BLOW-UPS
FOR
THE
HORN-KAPRANOV
PARAMETRIZATION
OF
THE
CLASSICAL
DISCRIMINANT
.
315
BY
EVGENY
MIKHALKIN,
VITALY
STEPANENKO
AND
AVGUST
TSIKH
1
INTRODUCTION
.
315
2
EXTREMAL
DISCRIMINANT
AND
FACTORIZATION
OF
ITS
TRUNCATIONS
.
318
3
PARAMETRIZATIONS
OF
ZERO
SETS
OF
DISCRIMINANTS
.322
4
BLOW-UPS
OF
HOM-KAPRANOV
PARAMETRIZATIONS
AND
PROOF
OF
THE
THEOREM
.
324
BIBLIOGRAPHY
.
328
20
EIGENVALUE
ESTIMATES
AND
ASYMPTOTICS
FOR
WEIGHTED
PSEUDODIFFERENTIAL
OPERATORS
WITH
SINGULAR
MEASURES
IN
THE
CRITICAL
CASE
.
331
BY
GRIGORI
ROZENBLUM
AND
EUGENE
SHARGORODSKY
1
INTRODUCTION
.
331
2
SETTING
AND
MAIN
RESULTS
.
333
3
SOME
REDUCTIONS
.
337
4
GEOMETRY
CONSIDERATIONS
.
341
5
ESTIMATES
.
344
6
APPROXIMATION
OF
THE
WEIGHT
.
350
7
THE
ASYMPTOTIC
FORMULA
.
351
BIBLIOGRAPHY
.
353
21
RELATIONS
BETWEEN
TWO
PARTS
OF
THE
SPECTRUM
OF
A
SCHRODINGER
OPERATOR
AND
OTHER
REMARKS
ON
THE
ABSOLUTE
CONTINUITY
OF
THE
SPECTRUM
IN
A
TYPICAL
CASE
.
355
BY
OLEG
SAFRONOV
1
INTRODUCTION
.
355
2
PROOF
OF
THEOREM
3.4
.
363
BIBLIOGRAPHY
.
364
22
BOGOLIUBOV
THEORY
FOR
MANY-BODY
QUANTUM
SYSTEMS
.
367
BY
BENJAMIN
SCHLEIN
1
INTRODUCTION
.
367
2
BOSE
GASES,
ENERGY
AND
DYNAMICS
.
368
3
THE
CORRELATION
ENERGY
OF
A
FERMI
GAS
.
377
4
DYNAMICS
OF
A
FROHLICH
POLARON
.
382
BIBLIOGRAPHY
.
386
23
A
STATISTICAL
THEORY
OF
HEAVY
ATOMS:
ASYMPTOTIC
BEHAVIOR
OF
THE ENERGY
AND
STABILITY
OF
MATTER
.
389
BY
HEINZ
SIEDENTOP
1
INTRODUCTION
.389
2
BOUNDS
ON
THE
ENERGY
.
392
XII
CONTENTS
3
STABILITY
OF
MATTER
.397
BIBLIOGRAPHY
.
401
24
HOMOGENIZATION
OF
THE
HIGHER-ORDER
SCHRODINGER-TYPE
EQUATIONS
WITH
PERIODIC
COEFFICIENTS
.
405
BY
TATIANA
SUSLINA
1
INTRODUCTION
.
405
2
ABSTRACT
OPERATOR-THEORETIC
SCHEME
.
408
3
PERIODIC
DIFFERENTIAL
OPERATORS
IN
L2(^
D
;
C
N
)
.
412
4
APPLICATION
OF
THE
ABSTRACT
RESULTS
TO
A(K)
.
415
5
APPROXIMATION
FOR
THE
OPERATOR
EXPONENTIAL
OF
A
.
421
6
HOMOGENIZATION
OF
THE
SCHRODINGER-TYPE
EQUATION
.
422
BIBLIOGRAPHY
.
425
25
TRACE
FORMULAS
FOR
THE
MODIFIED
MATHIEU
EQUATION
.
427
BY
LEON
A.
TAKHTAJAN
1
INTRODUCTION
.
427
2
GENERAL
CASE
.
430
3
EXAMPLES
.
434
4
EXISTENCE
OF
THE
SOLUTION
(X,
A)
.
440
BIBLIOGRAPHY
.
442
26
EIGENVALUE
ACCUMULATION
AND
BOUNDS
FOR
NON-SELFADJOINT
MATRIX
DIFFERENTIAL
OPERATORS
RELATED
TO
NLS
.
445
BY
CHRISTIANE
TRETTER
1
INTRODUCTION
.
445
2
AUXILIARY
SPECTRAL
BOUNDS
OF
INDEPENDENT
INTEREST
.
447
3
INVARIANT
SUBSPACES
AND
NON-REAL
SPECTRUM
.
450
BIBLIOGRAPHY
.
455
27
SCATTERING
THEORY
FOR
LAGUERRE
OPERATORS
.
457
BY
DIMITRI
R.
YAFAEV
1
INTRODUCTION
.
457
2
JACOBI
OPERATORS
AND
ORTHOGONAL
POLYNOMIALS
.
460
3
WAVE
OPERATORS
.
462
4
TIME
EVOLUTION
.
468
BIBLIOGRAPHY
.
478
LIST
OF
CONTRIBUTORS
.
,
.
479 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author2 | Exner, Pavel 1946- Frank, Rupert L. 1978- Gesztesy, Fritz 1953- Holden, Helge 1956- Weidl, Timo ca. 20./21. Jh |
| author2_role | edt edt edt edt edt |
| author2_variant | p e pe r l f rl rlf f g fg h h hh t w tw |
| author_GND | (DE-588)1012993876 (DE-588)134284410 (DE-588)1236600002 (DE-588)134200136 (DE-588)111693667 (DE-588)1095129147 |
| author_facet | Exner, Pavel 1946- Frank, Rupert L. 1978- Gesztesy, Fritz 1953- Holden, Helge 1956- Weidl, Timo ca. 20./21. Jh |
| building | Verbundindex |
| bvnumber | BV047498609 |
| classification_rvk | SK 540 SE 220 |
| ctrlnum | (OCoLC)1252774925 (DE-599)DNB1233748750 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| genre | (DE-588)4016928-5 Festschrift gnd-content (DE-588)4143413-4 Aufsatzsammlung gnd-content |
| genre_facet | Festschrift Aufsatzsammlung |
| id | DE-604.BV047498609 |
| illustrated | Illustrated |
| index_date | 2024-07-03T18:18:03Z |
| indexdate | 2024-07-10T09:13:46Z |
| institution | BVB |
| institution_GND | (DE-588)1066118477 |
| isbn | 9783985470075 3985470073 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032899712 |
| oclc_num | 1252774925 |
| open_access_boolean | |
| owner | DE-703 DE-11 DE-188 |
| owner_facet | DE-703 DE-11 DE-188 |
| physical | xii, 481 Seiten Illustrationen, Diagramme 25 cm |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | EMS Press |
| record_format | marc |
| series2 | EMS series of congress reports |
| spelling | Partial differential equations, spectral theory, and mathematical physics the Ari Laptev anniversary volume edited by Pavel Exner, Rupert L. Frank, Fritz Gesztesy, Helge Holden, Timo Weidl Berlin, Germany EMS Press [2021] © 2021 xii, 481 Seiten Illustrationen, Diagramme 25 cm txt rdacontent n rdamedia nc rdacarrier EMS series of congress reports heat kernel estimates nonlinear Schrödinger equation Lieb–Thirring inequality Bogoliubov theory Wehrl-type entropy inequalities Euler–Bardina equations d-bar problem Friedrichs inequality Bose–Einstein condensation wave packet evolution electron density estimates Brezis–Nirenberg problem Feshbach–Schur map stability of matter scattering theory Hardy inequality (DE-588)4016928-5 Festschrift gnd-content (DE-588)4143413-4 Aufsatzsammlung gnd-content Laptev, Ari 1950- (DE-588)1012993876 hnr Exner, Pavel 1946- (DE-588)134284410 edt Frank, Rupert L. 1978- (DE-588)1236600002 edt Gesztesy, Fritz 1953- (DE-588)134200136 edt Holden, Helge 1956- (DE-588)111693667 edt Weidl, Timo ca. 20./21. Jh. (DE-588)1095129147 edt European Mathematical Society Publishing House ETH-Zentrum SEW A27 (DE-588)1066118477 pbl Erscheint auch als Online-Ausgabe 978-3-9854750-7-0 (DE-604)BV047306383 B:DE-101 application/pdf https://d-nb.info/1233748750/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032899712&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Partial differential equations, spectral theory, and mathematical physics the Ari Laptev anniversary volume |
| subject_GND | (DE-588)4016928-5 (DE-588)4143413-4 |
| title | Partial differential equations, spectral theory, and mathematical physics the Ari Laptev anniversary volume |
| title_auth | Partial differential equations, spectral theory, and mathematical physics the Ari Laptev anniversary volume |
| title_exact_search | Partial differential equations, spectral theory, and mathematical physics the Ari Laptev anniversary volume |
| title_exact_search_txtP | Partial differential equations, spectral theory, and mathematical physics the Ari Laptev anniversary volume |
| title_full | Partial differential equations, spectral theory, and mathematical physics the Ari Laptev anniversary volume edited by Pavel Exner, Rupert L. Frank, Fritz Gesztesy, Helge Holden, Timo Weidl |
| title_fullStr | Partial differential equations, spectral theory, and mathematical physics the Ari Laptev anniversary volume edited by Pavel Exner, Rupert L. Frank, Fritz Gesztesy, Helge Holden, Timo Weidl |
| title_full_unstemmed | Partial differential equations, spectral theory, and mathematical physics the Ari Laptev anniversary volume edited by Pavel Exner, Rupert L. Frank, Fritz Gesztesy, Helge Holden, Timo Weidl |
| title_short | Partial differential equations, spectral theory, and mathematical physics |
| title_sort | partial differential equations spectral theory and mathematical physics the ari laptev anniversary volume |
| title_sub | the Ari Laptev anniversary volume |
| topic_facet | Festschrift Aufsatzsammlung |
| url | https://d-nb.info/1233748750/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032899712&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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Indexes