The asymptotic distribution of eigenvalues of partial differential operators:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
1998
|
| Edition: | Repr. with corr. |
| Series: | Translations of mathematical monographs
155 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | XIII, 354 S. graph. Darst. |
| ISBN: | 0821809210 |
Staff View
MARC
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| 240 | 1 | 0 | |a Asimptotičeskoe raspredelenie sobstvennych značenij differencial'nych operatorov v častnych proizvodnych |
| 245 | 1 | 0 | |a The asymptotic distribution of eigenvalues of partial differential operators |c Yu. Safarov ; D. Vassiliev |
| 250 | |a Repr. with corr. | ||
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1998 | |
| 300 | |a XIII, 354 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Translations of mathematical monographs |v 155 | |
| 500 | |a Aus dem Russ. übers. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
xi
Chapter
1.
Main Results
1
1.1.
Statement of the spectral problem
1
1.2.
One-term asymptotic formula for
Λ^(λ)
9
1.3.
Hamiltonian billiards I: basic definitions and results
11
1.4.
Hamiltonian billiards II
:
reflection matrix
27
1.5.
Hamiltonian billiards
III: Maslov
index
32
1.6.
Classical two-term asymptotic formula for N(X)
37
1.7.
Nonclassical two-term asymptotic formulae for N(X)
49
1.8.
Two-term asymptotic formulae for the spectral function
56
Chapter
2.
Oscillatory Integrals
63
2.1.
Local oscillatory integrals and pseudodifferential operators
63
2.2.
Global oscillatory integrals
70
2.3.
Homogeneous canonical transformations
74
2.4.
Phase functions associated with homogeneous canonical transfor¬
mations
78
2.5.
Restriction of phase functions to the boundary
89
2.6.
Extension of phase functions from the boundary
91
2.7.
Standard oscillatory integrals associated with homogeneous canon¬
ical transformations
100
2.8.
Boundary layer oscillatory integrals associated with homogeneous
canonical transformations
112
2.9.
Boundary oscillatory integrals associated with homogeneous ca¬
nonical transformations
115
2.10.
Parameter-dependent oscillatory integrals
119
Chapter
3.
Construction of the Wave Group
129
3.1.
Characteristic properties of distributions associated with the wave
group
130
3.2.
Representation of the wave group by means of oscillatory integrals:
sufficient conditions
140
3.3.
Representation of the wave group by means of oscillatory integrals:
effective construction for manifolds without boundary
142
3.4.
Representation of the wave group by means of oscillatory integrals:
effective construction for manifolds with boundary
148
3.5.
Construction of the wave group when the source is close to the
boundary
161
viii
(ONI KN
IS
Chapter
4.
Singularities of the Wave Group Hi
4.1.
Singularities of Lagrangian «listributUrns
№&
4.2.
Singularity of the wave group at
t ~
0 176
4.3.
Singularities of the wave group at
t
Φ
0
for admissible psottdodif-
ferential cut-offs
J
79
4.4.
Singularities of the wave group at
f
Φ-
0
for nonadtmssible pseu-
dodifferential cut-offs
183
4.5.
Singularity of the wave group at
t
= 0
when the .source is close to
the boundary
190
Chapter
5.
Proof of Main Results
193
5.1.
Partition of the manifold
M
into three zones
193
5.2.
Asymptotics of the trace of the spectral projection in the interior
zone
198
5.3.
Asymptotics of the trace of the spectral projection in the interme¬
diate zone
201
5.4.
Asymptotics of the trace of the spectral projection in the boundary
zone
205
5.5.
Asymptotics of the spectral function
224
Chapter
6.
Mechanical Applications
229
6.1.
Membranes and acoustic resonators
229
6.2.
Elastic plates
230
6.3.
Two- and three-dimensional elasticity
236
6.4.
Elastic shells
239
6.5.
Hydroelasticity
247
Appendix A. Spectral Problem on the Half-line
by A.
Holst 251
A.I. Basic facts
251
A.2. The reflection matrix
263
A.3. Trace formulae
276
A.4. Dependence on parameters
292
Appendix B. Fourier Tauberian Theorems
by M. Levitin
297
B.I. Introductory remarks
297
B.2. Basic theorem
298
B.3. Rough estimate for the nonzero singularities
300
B.4. General refined theorem
301
B.5. Special version of the general refined theorem
304
Appendix C. Stationary Phase Formula
307
Appendix D. Hamiltonian Billiards
:
Proofs
313
D.I.
Measure of awkward starting points
313
D.2. Dead-end trajectories
318
D.3. Convexity and concavity
321
D.4. Measurability of sets and functions
324
D.5. Lengths of loops and periodic trajectories
326
D.6. Masbv index
328
CONTENTS ix
Appendix
E.
Factorization of Smooth Functions and Taylor-type Formulae
335
References
343
Principal Notation
349
Index
353
|
| any_adam_object | 1 |
| author | Safarov, Ju Vasil'ev, D. |
| author_facet | Safarov, Ju Vasil'ev, D. |
| author_role | aut aut |
| author_sort | Safarov, Ju |
| author_variant | j s js d v dv |
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| bvnumber | BV012775974 |
| classification_rvk | SK 620 |
| ctrlnum | (OCoLC)174554031 (DE-599)BVBBV012775974 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.7242 |
| dewey-search | 515/.7242 |
| dewey-sort | 3515 47242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Repr. with corr. |
| format | Book |
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| id | DE-604.BV012775974 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:33:27Z |
| institution | BVB |
| isbn | 0821809210 |
| language | English |
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| physical | XIII, 354 S. graph. Darst. |
| publishDate | 1998 |
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| publishDateSort | 1998 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Safarov, Ju. Verfasser aut Asimptotičeskoe raspredelenie sobstvennych značenij differencial'nych operatorov v častnych proizvodnych The asymptotic distribution of eigenvalues of partial differential operators Yu. Safarov ; D. Vassiliev Repr. with corr. Providence, RI American Math. Soc. 1998 XIII, 354 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 155 Aus dem Russ. übers. Eigenwert (DE-588)4151200-5 gnd rswk-swf Eigenwertproblem (DE-588)4013802-1 gnd rswk-swf Partieller Differentialoperator (DE-588)4173439-7 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Distribution Funktionalanalysis (DE-588)4070505-5 gnd rswk-swf Asymptotische Wahrscheinlichkeitsverteilung (DE-588)4519235-2 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Partieller Differentialoperator (DE-588)4173439-7 s Eigenwert (DE-588)4151200-5 s Asymptotische Wahrscheinlichkeitsverteilung (DE-588)4519235-2 s Distribution Funktionalanalysis (DE-588)4070505-5 s DE-604 Partielle Differentialgleichung (DE-588)4044779-0 s Eigenwertproblem (DE-588)4013802-1 s Asymptotik (DE-588)4126634-1 s 1\p DE-604 Vasil'ev, D. Verfasser aut Translations of mathematical monographs 155 (DE-604)BV000002394 155 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008688251&sequence=000002&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 | Safarov, Ju Vasil'ev, D. The asymptotic distribution of eigenvalues of partial differential operators Translations of mathematical monographs Eigenwert (DE-588)4151200-5 gnd Eigenwertproblem (DE-588)4013802-1 gnd Partieller Differentialoperator (DE-588)4173439-7 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd Asymptotische Wahrscheinlichkeitsverteilung (DE-588)4519235-2 gnd Asymptotik (DE-588)4126634-1 gnd |
| subject_GND | (DE-588)4151200-5 (DE-588)4013802-1 (DE-588)4173439-7 (DE-588)4044779-0 (DE-588)4070505-5 (DE-588)4519235-2 (DE-588)4126634-1 |
| title | The asymptotic distribution of eigenvalues of partial differential operators |
| title_alt | Asimptotičeskoe raspredelenie sobstvennych značenij differencial'nych operatorov v častnych proizvodnych |
| title_auth | The asymptotic distribution of eigenvalues of partial differential operators |
| title_exact_search | The asymptotic distribution of eigenvalues of partial differential operators |
| title_full | The asymptotic distribution of eigenvalues of partial differential operators Yu. Safarov ; D. Vassiliev |
| title_fullStr | The asymptotic distribution of eigenvalues of partial differential operators Yu. Safarov ; D. Vassiliev |
| title_full_unstemmed | The asymptotic distribution of eigenvalues of partial differential operators Yu. Safarov ; D. Vassiliev |
| title_short | The asymptotic distribution of eigenvalues of partial differential operators |
| title_sort | the asymptotic distribution of eigenvalues of partial differential operators |
| topic | Eigenwert (DE-588)4151200-5 gnd Eigenwertproblem (DE-588)4013802-1 gnd Partieller Differentialoperator (DE-588)4173439-7 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd Asymptotische Wahrscheinlichkeitsverteilung (DE-588)4519235-2 gnd Asymptotik (DE-588)4126634-1 gnd |
| topic_facet | Eigenwert Eigenwertproblem Partieller Differentialoperator Partielle Differentialgleichung Distribution Funktionalanalysis Asymptotische Wahrscheinlichkeitsverteilung Asymptotik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008688251&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
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