Mathematical methods in physics: distributions, Hilbert space operators, and variational methods
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2003
|
| Series: | Progress in mathematical physics
26 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Erweitere Version von: Blanchard, Philippe: Distributionen und Hilbertraumoperatoren (1993) |
| Physical Description: | XIII, 471 S. |
| ISBN: | 3764342285 0817642285 |
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MARC
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| 100 | 1 | |a Blanchard, Philippe |d 1942- |e Verfasser |0 (DE-588)120744635 |4 aut | |
| 240 | 1 | 0 | |a Distributionen und Hilbertraumoperatoren - Mathematische Methoden der Physik <engl., rev. u. erw.> |
| 245 | 1 | 0 | |a Mathematical methods in physics |b distributions, Hilbert space operators, and variational methods |c Philippe Blanchard ; Erwin Brüning |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2003 | |
| 300 | |a XIII, 471 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in mathematical physics |v 26 | |
| 500 | |a Erweitere Version von: Blanchard, Philippe: Distributionen und Hilbertraumoperatoren (1993) | ||
| 650 | 4 | |a Physique mathématique | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 0 | 7 | |a Distributionstheorie |0 (DE-588)4150254-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Hilbert-Raum |0 (DE-588)4159850-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematische Physik |0 (DE-588)4037952-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Linearer Operator |0 (DE-588)4167721-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Distribution |g Funktionalanalysis |0 (DE-588)4070505-5 |2 gnd |9 rswk-swf |
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| 787 | 0 | 8 | |i Based on German ed. |a Blanchard, Philippe |t Distributionen und Hilbertraumoperatoren |
| 830 | 0 | |a Progress in mathematical physics |v 26 |w (DE-604)BV013823265 |9 26 | |
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Record in the Search Index
| _version_ | 1808226396445605888 |
|---|---|
| adam_text |
CONTENTS
PREFACE
XV
NOTATION
XVII
I
DISTRIBUTIONS
1
1
INTRODUCTION
3
2
SPACES
OF
TEST
FUNCTIONS
7
2.1
HAUSDORFF
LOCALLY
CONVEX
TOPOLOGICAL
VECTOR
SPACES
.
7
2.1.1
EXAMPLES
OF
HLCTVS
.
14
2.1.2
CONTINUITY AND
CONVERGENCE
IN
A
HLCVTVS
.
15
2.2
BASIC
TEST
FUNCTION
SPACES
OF
DISTRIBUTION
THEORY
.
18
2.2.1
THE
TEST
FUNCTION
SPACE
P(Q)
OF
C
00
FUNCTIONS
OF
COMPACT
SUPPORT
.
19
2.2.2
THE
TEST
FUNCTION
SPACE
S(Q)
OF
STRONGLY
DECREASING
C
-FUNCTIONS
ON
Q
.
20
2.2.3
THE
TEST
FUNCTION
SPACE
(Q)
OF
ALL
C-FUNCTIONS
ON
2
.
.
21
2.2.4
RELATION
BETWEEN
THE
TEST
FUNCTION
SPACES
2 (Q),
S(Q),
AND(Q)
.
22
2.3
EXERCISES
.
22
VIII
CONTENTS
3
SCHWARTZ
DISTRIBUTIONS
27
3.1
THE
TOPOLOGICAL
DUAL
OF
A
HLCTVS
.
27
3.2
DEFINITION
OF
DISTRIBUTIONS
.
29
3.2.1
THE
REGULAR
DISTRIBUTIONS
.
31
3.2.2
SOME
STANDARD
EXAMPLES
OF
DISTRIBUTIONS
.
33
3.3
CONVERGENCE
OF
SEQUENCES
AND
SERIES
OF
DISTRIBUTIONS
.
35
3.4
LOCALIZATION
OF
DISTRIBUTIONS
.
40
3.5
TEMPERED
DISTRIBUTIONS
AND
DISTRIBUTIONS
WITH
COMPACT
SUPPORT
.
.
42
3.6
EXERCISES
.
44
4
CALCULUS
FOR
DISTRIBUTIONS
47
4.1
DIFFERENTIATION
.
48
4.2
MULTIPLICATION
.
51
4.3
TRANSFORMATION
OF
VARIABLES
.
54
4.4
SOME
APPLICATIONS
.
56
4.4.1
DISTRIBUTIONS
WITH
SUPPORT
IN
A
POINT
.
56
4.4.2
RENORMALIZATION
OF
()+
=
^
.
58
4.5
EXERCISES
.
60
5
DISTRIBUTIONS
AS
DERIVATIVES
OF
FUNCTIONS
63
5.1
WEAK
DERIVATIVES
.
63
5.2
STRUCTURE
THEOREM
FOR
DISTRIBUTIONS
.
65
5.3
RADON
MEASURES
.
67
5.4
THE
CASE
OF
TEMPERED
AND
COMPACTLY
SUPPORTED
DISTRIBUTIONS
.
68
5.5
EXERCISES
.
70
6
TENSOR
PRODUCTS
71
6.1
TENSOR
PRODUCT
FOR
TEST
FUNCTION
SPACES
.
71
6.2
TENSOR
PRODUCT
FOR
DISTRIBUTIONS
.
75
6.3
EXERCISES
.
81
7
CONVOLUTION
PRODUCTS
83
7.1
CONVOLUTION
OF
FUNCTIONS
.
83
7.2
REGULARIZATION
OF
DISTRIBUTIONS
.
87
7.3
CONVOLUTION
OF
DISTRIBUTIONS
.
90
7.4
EXERCISES
.
96
8
APPLICATIONS
OF
CONVOLUTION
99
8.1
SYMBOLIC
CALCULUS
-
ORDINARY
LINEAR
DIFFERENTIAL
EQUATIONS
.
100
8.2
INTEGRAL
EQUATION
OF
VOLTERRA
.
104
8.3
LINEAR
PARTIAL
DIFFERENTIAL
EQUATIONS
WITH
CONSTANT
COEFFICIENTS
.
.
.
105
8.4
ELEMENTARY
SOLUTIONS
OF
PARTIAL
DIFFERENTIAL
OPERATORS
.
108
8.4.1
THE
LAPLACE
OPERATOR
A
N
=
"=I
IN
R"
.
108
8.4.2
THE
PDE
OPERATOR
-
A
N
OF
THE
HEAT
EQUATION
IN
R
N+1
.
110
8.4.3
THE
WAVE
OPERATOR
04
=
3
Q
-
A3
IN
R
4
.
ILL
8.5
EXERCISES
.
113
CONTENTS
IX
9
HOLOMORPHIC
FUNCTIONS^
115
9.1
HYPO-ELLIPTICITY
OF
D
.
115
9.2 CAUCHY
THEORY
.
118
9.3
SOME
PROPERTIES
OF
HOLOMORPHIC
FUNCTIONS
.
121
9.4
EXERCISES
.
126
10
FOURIER
TRANSFORMATION
127
10.1
FOURIER
TRANSFORMATION
FOR
INTEGRABLE
FUNCTIONS
.
128
10.2
FOURIER
TRANSFORMATION
ON
S(R")
.
134
10.3
FOURIER
TRANSFORMATION
FOR
TEMPERED
DISTRIBUTIONS
.
137
10.4
SOME
APPLICATIONS
.
143
10.4.1
EXAMPLES
OF
TEMPERED
ELEMENTARY
SOLUTIONS
.
145
10.4.2
SUMMARY
OF
PROPERTIES
OF
THE
FOURIER
TRANSFORMATION
.
.
.
148
10.5
EXERCISES
.
149
11
DISTRIBUTIONS
AND
ANALYTIC
FUNCTIONS
153
11.1
DISTRIBUTIONS
AS
BOUNDARY
VALUES
OF
ANALYTIC
FUNCTIONS
.
153
11.2
EXERCISES
.
157
12
OTHER
SPACES
OF
GENERALIZED
FUNCTIONS
159
12.1
GENERALIZED
FUNCTIONS
OF
GELFAND
TYPE
S
.
160
12.2
HYPERFUNCTIONS
AND
FOURIER
HYPERFUNCTIONS
.
164
12.3
ULTRADISTRIBUTIONS
.
167
II
HILBERT
SPACE
OPERATORS
171
13
HILBERT
SPACES:
A
BRIEF
HISTORICAL
INTRODUCTION
173
13.1
SURVEY:
HILBERT
SPACES
.
173
13.2
SOME
HISTORICAL
REMARKS
.
179
13.3
HILBERT
SPACES
AND
PHYSICS
.
181
14
INNER
PRODUCT
SPACES
AND
HILBERT
SPACES
185
14.1
INNER
PRODUCT
SPACES
.
185
14.1.1
BASIC
DEFINITIONS
AND
RESULTS
.
186
14.1.2
BASIC
TOPOLOGICAL
CONCEPTS
.
190
14.1.3
ON
THE
RELATION
BETWEEN
NORMED
SPACES
AND
INNER
PRODUCT
SPACES
.
192
14.1.4
EXAMPLES
OF
HILBERT
SPACES
.
193
14.2
EXERCISES
.
196
15
GEOMETRY
OF
HILBERT
SPACES
199
15.1
ORTHOGONAL
COMPLEMENTS
AND
PROJECTIONS
.
199
15.2
GRAM
DETERMINANTS
.
203
15.3
THE
DUAL
OF
A
HILBERT
SPACE
.
205
15.4
EXERCISES
.
209
X
CONTENTS
16
SEPARABLE
HILBERT
SPACES
211
16.1
BASIC
FACTS
.
211
16.2
WEIGHT
FUNCTIONS
AND
ORTHOGONAL
POLYNOMIALS
.
217
16.3
EXAMPLES
OF
COMPLETE
ORTHONORMAL
SYSTEMS
FOR
L
2
(Z,
PDX)
.
221
16.4
EXERCISES
.
223
17
DIRECT
SUMS
AND
TENSOR
PRODUCTS
227
17.1
DIRECT
SUMS
OF
HILBERT
SPACES
.
227
17.2
TENSOR
PRODUCTS
.
229
17.3
SOME
APPLICATIONS
OF
TENSOR
PRODUCTS
AND
DIRECT
SUMS
.
232
17.3.1
STATE
SPACE
OF
PARTICLES
WITH
SPIN
.
232
17.3.2
STATE
SPACE
OF
MULTI-PARTICLE
SYSTEMS
.
233
17.4
EXERCISES
.
234
18
TOPOLOGICAL
ASPECTS
235
18.1
COMPACTNESS
.
235
18.2
THE
WEAK
TOPOLOGY
.
237
18.3
EXERCISES
.
245
19
LINEAR
OPERATORS
247
19.1
BASIC
FACTS
.
247
19.2
ADJOINTS,
CLOSED
AND
CLOSABLE
OPERATORS
.
250
19.3
SYMMETRIC
AND
SELF-ADJOINT
OPERATORS
.
256
19.4
EXAMPLES
.
259
19.4.1
OPERATOR
OF
MULTIPLICATION
.
259
19.4.2
MOMENTUM
OPERATOR
.
260
19.4.3
FREE
HAMILTON
OPERATOR
.
261
19.5
EXERCISES
.
262
20
QUADRATIC
FORMS
265
20.1
BASIC
CONCEPTS.
EXAMPLES
.
265
20.2
REPRESENTATION
OF
QUADRATIC
FORMS
.
268
20.3
SOME
APPLICATIONS
.
271
20.4
EXERCISES
.
274
21
BOUNDED
LINEAR
OPERATORS
275
21.1
PRELIMINARIES
.
275
21.2
EXAMPLES
.
277
21.3
THE
SPACE
(H,
IC)
OF
BOUNDED
LINEAR
OPERATORS
.
.
.
.
281
21.4
THE
C*-ALGEBRA
93(H)
.
283
21.5
CALCULUS
IN
THE
C*-ALGEBRA
93(H)
.
286
21.5.1
PRELIMINARIES
.
286
21.5.2
POLAR
DECOMPOSITION
OF
OPERATORS
.
288
21.6
EXERCISES
.
289
CONTENTS
XI
22
SPECIAL
CLASSES
OF
BOUNDED
OPERATORS
293
22.1
PROJECTION
OPERATORS
.
293
22.2
UNITARY
OPERATORS
.
297
22.2.1
ISOMETRIES
.
297
22.2.2
UNITARY
OPERATORS
.
297
22.2.3
EXAMPLES
OF
UNITARY
OPERATORS
.
300
22.3
COMPACT
OPERATORS
.
300
22.4
TRACE
CLASS
OPERATORS
.
304
22.5
SOME
APPLICATIONS
IN
QUANTUM
MECHANICS
.
308
22.6
EXERCISES
.
311
23
SELF-ADJOINT
HAMILTON
OPERATORS
313
23.1
KATO
PERTURBATIONS
.
314
23.2
KATO
PERTURBATIONS
OF
THE
FREE
HAMILTONIAN
.
315
23.3
EXERCISES
.
316
24
ELEMENTS
OF
SPECTRAL
THEORY
317
24.1
BASIC
CONCEPTS
AND
RESULTS
.
318
24.2
THE
SPECTRUM
OF
SPECIAL
OPERATORS
.
322
24.3
COMMENTS
ON
SPECTRAL
PROPERTIES
OF
LINEAR
OPERATORS
.
324
24.4
EXERCISES
.
325
25
SPECTRAL
THEORY
OF
COMPACT
OPERATORS
327
25.1
THE
RESULTS
OF
RIESZ
AND
SCHAUDER
.
327
25.2
THE
FREDHOLM
ALTERNATIVE
.
329
25.3
EXERCISES
.
331
26
THE
SPECTRAL
THEOREM
333
26.1
GEOMETRIC
CHARACTERIZATION
OF
SELF-ADJOINTNESS
.
334
26.1.1
PRELIMINARIES
.
334
26.1.2
SUBSPACES
OF
CONTROLLED
GROWTH
.
335
26.2
SPECTRAL
FAMILIES
AND
THEIR
INTEGRALS
.
340
26.2.1
SPECTRAL
FAMIHES
.
341
26.2.2
INTEGRATION
WITH
RESPECT
TO
A
SPECTRAL
FAMILY
.
342
26.3
THE
SPECTRAL
THEOREM
.
347
26.4
SOME
APPLICATIONS
.
351
26.5
EXERCISES
.
353
27
SOME
APPLICATIONS
OF
THE
SPECTRAL
REPRESENTATION
355
27.1
FUNCTIONAL
CALCULUS
.
355
27.2
DECOMPOSITION
OF
THE
SPECTRUM
-
SPECTRAL
SUBSPACES
.
357
27.3
INTERPRETATION
OF
THE
SPECTRUM
OF
A
SELF-ADJOINT
HAMILTONIAN
.
364
27.4
EXERCISES
.
369
XII
CONTENTS
M
VARIATIONAL
METHODS
371
28
INTRODUCTION
373
28.1
ROADS
TO
CALCULUS
OF
VARIATIONS
.
374
28.2
CLASSICAL
APPROACH
VERSUS
DIRECT
METHODS
.
375
28.3
THE
OBJECTIVES
OF
THE
FOLLOWING
CHAPTERS
.
378
29
DIRECT
METHODS
IN
THE
CALCULUS
OF
VARIATIONS
379
29.1
GENERAL
EXISTENCE
RESULTS
.
379
29.2
MINIMIZATION
IN
BANACH
SPACES
.
381
29.3
MINIMIZATION
OF
SPECIAL
CLASSES
OF
FUNCTIONALS
.
383
29.4
EXERCISES
.
384
30
DIFFERENTIAL
CALCULUS
ON
BANACH
SPACES
AND
EXTREMA
OF
FUNCTIONS
387
30.1
THE
FRDCHET
DERIVATIVE
.
388
30.2
EXTREMA
OF
DIFFERENTIABLE
FUNCTIONS
.
393
30.3
CONVEXITY
AND
MONOTONICITY
.
395
30.4
GATEAUX
DERIVATIVES
AND
VARIATIONS
.
397
30.5
EXERCISES
.
401
31
CONSTRAINED
MINIMIZATION
PROBLEMS
(METHOD
OF
LAGRANGE
MULTIPLIERS)
403
31.1
GEOMETRICAL
INTERPRETATION
OF
CONSTRAINED
MINIMIZATION
.
404
31.2
TANGENT
SPACES
OF
LEVEL
SURFACES
.
405
31.3
EXISTENCE
OF
LAGRANGE
MULTIPLIERS
.
407
31.3.1
COMMENTS
ON
DIDO
'
S
PROBLEM
.
409
31.4
EXERCISES
.
410
32
BOUNDARY
AND
EIGENVALUE
PROBLEMS
413
32.1
MINIMIZATION
IN
HILBERT
SPACES
.
413
32.2
THE
DIRICHLET-LAPLACE
OPERATOR
AND
OTHER
ELLIPTIC
DIFFERENTIAL
OPERATORS
.
416
32.3
NONLINEAR
CONVEX
PROBLEMS
.
420
32.4
EXERCISES
.
426
33
DENSITY
FUNCTIONAL
THEORY
OF
ATOMS
AND
MOLECULES
429
33.1
INTRODUCTION
.
429
33.2
SEMI-CLASSICAL
THEORIES
OF
DENSITY
FUNCTIONALS
.
431
33.3
HOHENBERG-KOHN
THEORY
.
432
33.3.1
HOHENBERG-KOHN
VARIATIONAL
PRINCIPLE
.
435
33.3.2
THE
KOHN-SHAM
EQUATIONS
.
437
33.4
EXERCISES
.
438
CONTENTS
XIII
IV
APPENDIX
439
A
COMPLETION
OF
METRIC
SPACES
441
B
METRIZABLE
LOCALLY
CONVEX
TOPOLOGICAL
VECTOR
SPACES
445
C
THE
THEOREM
OF
BAIRE
447
C.L
THE
UNIFORM
BOUNDEDNESS
PRINCIPLE
.
449
C.2
THE
OPEN
MAPPING
THEOREM
.
452
D
BILINEAR
FUNCTIONALS
455
REFERENCES
457
INDEX
465 |
| any_adam_object | 1 |
| author | Blanchard, Philippe 1942- Brüning, Erwin |
| author_GND | (DE-588)120744635 (DE-588)124673198 |
| author_facet | Blanchard, Philippe 1942- Brüning, Erwin |
| author_role | aut aut |
| author_sort | Blanchard, Philippe 1942- |
| author_variant | p b pb e b eb |
| building | Verbundindex |
| bvnumber | BV016463364 |
| callnumber-first | Q - Science |
| callnumber-label | QC20 |
| callnumber-raw | QC20 |
| callnumber-search | QC20 |
| callnumber-sort | QC 220 |
| callnumber-subject | QC - Physics |
| classification_rvk | SK 950 SK 600 |
| classification_tum | PHY 011 |
| ctrlnum | (OCoLC)49921962 (DE-599)BVBBV016463364 |
| dewey-full | 530.15 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.15 |
| dewey-search | 530.15 |
| dewey-sort | 3530.15 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV016463364 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-24T00:24:32Z |
| institution | BVB |
| isbn | 3764342285 0817642285 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010178379 |
| oclc_num | 49921962 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-29T DE-19 DE-BY-UBM DE-384 DE-20 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-29T DE-19 DE-BY-UBM DE-384 DE-20 DE-634 DE-83 DE-11 DE-188 |
| physical | XIII, 471 S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematical physics |
| series2 | Progress in mathematical physics |
| spelling | Blanchard, Philippe 1942- Verfasser (DE-588)120744635 aut Distributionen und Hilbertraumoperatoren - Mathematische Methoden der Physik <engl., rev. u. erw.> Mathematical methods in physics distributions, Hilbert space operators, and variational methods Philippe Blanchard ; Erwin Brüning Boston [u.a.] Birkhäuser 2003 XIII, 471 S. txt rdacontent n rdamedia nc rdacarrier Progress in mathematical physics 26 Erweitere Version von: Blanchard, Philippe: Distributionen und Hilbertraumoperatoren (1993) Physique mathématique Mathematische Physik Mathematical physics Distributionstheorie (DE-588)4150254-1 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Linearer Operator (DE-588)4167721-3 gnd rswk-swf Distribution Funktionalanalysis (DE-588)4070505-5 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 s DE-604 Distributionstheorie (DE-588)4150254-1 s Hilbert-Raum (DE-588)4159850-7 s Linearer Operator (DE-588)4167721-3 s Distribution Funktionalanalysis (DE-588)4070505-5 s 1\p DE-604 Brüning, Erwin Verfasser (DE-588)124673198 aut Based on German ed. Blanchard, Philippe Distributionen und Hilbertraumoperatoren Progress in mathematical physics 26 (DE-604)BV013823265 26 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010178379&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Blanchard, Philippe 1942- Brüning, Erwin Mathematical methods in physics distributions, Hilbert space operators, and variational methods Progress in mathematical physics Physique mathématique Mathematische Physik Mathematical physics Distributionstheorie (DE-588)4150254-1 gnd Hilbert-Raum (DE-588)4159850-7 gnd Mathematische Physik (DE-588)4037952-8 gnd Linearer Operator (DE-588)4167721-3 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd |
| subject_GND | (DE-588)4150254-1 (DE-588)4159850-7 (DE-588)4037952-8 (DE-588)4167721-3 (DE-588)4070505-5 |
| title | Mathematical methods in physics distributions, Hilbert space operators, and variational methods |
| title_alt | Distributionen und Hilbertraumoperatoren - Mathematische Methoden der Physik <engl., rev. u. erw.> |
| title_auth | Mathematical methods in physics distributions, Hilbert space operators, and variational methods |
| title_exact_search | Mathematical methods in physics distributions, Hilbert space operators, and variational methods |
| title_full | Mathematical methods in physics distributions, Hilbert space operators, and variational methods Philippe Blanchard ; Erwin Brüning |
| title_fullStr | Mathematical methods in physics distributions, Hilbert space operators, and variational methods Philippe Blanchard ; Erwin Brüning |
| title_full_unstemmed | Mathematical methods in physics distributions, Hilbert space operators, and variational methods Philippe Blanchard ; Erwin Brüning |
| title_short | Mathematical methods in physics |
| title_sort | mathematical methods in physics distributions hilbert space operators and variational methods |
| title_sub | distributions, Hilbert space operators, and variational methods |
| topic | Physique mathématique Mathematische Physik Mathematical physics Distributionstheorie (DE-588)4150254-1 gnd Hilbert-Raum (DE-588)4159850-7 gnd Mathematische Physik (DE-588)4037952-8 gnd Linearer Operator (DE-588)4167721-3 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd |
| topic_facet | Physique mathématique Mathematische Physik Mathematical physics Distributionstheorie Hilbert-Raum Linearer Operator Distribution Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010178379&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013823265 |
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