Spectral theory, microlocal analysis, singular manifolds
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| Format: | Buch |
|---|---|
| Sprache: | German |
| Veröffentlicht: |
Berlin
Akad.-Verl.
1997
|
| Schriftenreihe: | Mathematical topics
14 : Advances in partial differential equations |
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| Online-Zugang: | Inhaltsverzeichnis |
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| 245 | 1 | 0 | |a Spectral theory, microlocal analysis, singular manifolds |c ed. by Michael Demuth ... |
| 264 | 1 | |a Berlin |b Akad.-Verl. |c 1997 | |
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| 650 | 4 | |a Calcul pseudo-différentiel | |
| 650 | 4 | |a Capacité | |
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| 650 | 7 | |a Opérateurs intégraux |2 ram | |
| 650 | 4 | |a Spectre (Mathématiques) | |
| 650 | 7 | |a Théorie spectrale (mathématiques) |2 ram | |
| 650 | 4 | |a Variété singulière | |
| 650 | 4 | |a Microlocal analysis | |
| 650 | 4 | |a Spectral theory (Mathematics) | |
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Datensatz im Suchindex
| _version_ | 1804126056769126400 |
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| adam_text | Contents
Capacity and Spectral Theory 12
M. Demuth, I. McGillivray, and A. Noll
1 Introduction 12
2 Capacity and regular Dirichlet forms, possible generalizations 13
2.1 General theory 13
Definitions 13
Regular Dirichlet form with measure perturbations 16
Stochastic representation of the equilibrium potential 19
2.2 Generalizations 22
The capacity of a non regular, non symmetric Dirichlet form . 23
Capacities on Rd 25
The capacity of a subspace 26
3 Capacity and Dirichlet spaces 28
4 Capacity and eigenvalues of self adjoint operators 32
4.1 Ground state shift for sets of finite capacity 33
4.2 The ground state shift in the abstract Hilbert space setting . . 39
4.3 Asymptotics of the Dirichlet perturbed ground state 41
5 Capacity, differences of semigroups, scattering theory 46
5.1 The integral trace of an integral operator 46
5.2 Complete scattering systems 52
5.3 Scattering phases and capacity 58
6 Appendix 63
6.1 Markov processes associated to Dirichlet forms 63
6.2 Basics on regular Dirichlet forms 67
References 72
8 Contents
Some Results on the Scattering of Weakly Interacting Solitons for Non¬
linear Schrodinger Equations 78
G. Perehnan
Introduction 78
1 Asymptotic behavior of solutions of nonlinear equation 82
1.1 Preliminary facts and formulation of the result 82
1.1.1. Solitons 82
1.1.2. Linearization on the solitons 83
1.1.3. Description of the problem 84
1.2 Separation of the motion 85
1.2.1. Orthogonality conditions 85
1.2.2. Differential equations for the components of the decom¬
position 86
1.3 Preliminary estimates 88
1.3.1. Nonlinear equation 88
1.3.2. Estimates of linear evolution 89
1.4 Estimates of the majorants 90
1.4.1. Estimates of the solitons parameters 90
1.4.2. Estimates of D 91
1.4.3. Estimates of the dispersive part of x 94
1.4.4. Closing of the estimates 96
1.5 Scattering 98
1.6 Cauchy problem with initial conditions at t = —oo 99
2 Properties of the linearized equation 103
2.1 One soliton linearization 104
2.1.1. Spectral properties of the operator L 104
2.1.2. Linear one soliton evolution Ill
2.2 Solutions of two soliton linearization with the standard behav¬
ior as t — +co 113
2.2.1. The solutions Qi of the discrete spectrum 114
2.2.2. Dispersive solutions 115
2.3 Asymptotic completeness for the two soliton linearization . . . 118
2.3.1. The operator K~x{0) 118
2.3.2. Proof of proposition 2.3.1 126
2.4 Estimates of two soliton evolution 132
References 135
Weakly Smooth Nonselfadjoint Spectral Elliptic Boundary Problems 138
M. Agranovich, R. Derik, and M. Faierman
1 Introduction 138
2 Basic theorem and smoothness assumptions 146
3 Simplest spectral consequences 153
4 Asymptotics of powers of the resolvent 156
Contents 9
5 Asymptotics of powers of the resolvent for weakly smooth problems . . 165
6 Rough and precise asymptotics of eigenvalues 172
7 Boundary problems with transmission conditions 179
8 Boundary problems with indefinite weight 180
9 Some generalizations 186
Appendix 186
References 196
Integral Operators with Singular Canonical Relations 200
A. Comech
1 Oscillatory integral operators with singularities 200
1.1 Introduction 200
1.2 Relation with Fourier integral operators 208
1.3 Pseudoconvexity 212
1.4 Geometry of the canonical relation 215
1.5 Cotlar Stein Almost Orthogonality 223
1.6 Operators with one sided Whitney fold 224
2 Radon transform of Melrose Taylor 230
2.1 Background from scattering theory 230
2.2 Regularity properties of Ti^j. 234
2.3 Associated canonical relation 236
2.4 Isolated precise points 239
2.5 Proof for the general case 242
2.6 Regularity properties of the operator F 247
References 247
Pseudo Differential Calculus in the Fourier Edge Approach on Non
Compact Manifolds 249
Ch. Dorschfeldt, U. Grieme, and B. W. Schulze
Introduction 249
1 The global Fourier edge pseudo differential operators 251
1.1 Weighted operators and abstract wedge Sobolev spaces .... 251
1.2 The case of Hilbert spaces 260
1.3 The case of Banach spaces 270
1.4 Ellipticity and parametrices 274
2 Operators on manifolds with conical exits 277
2.1 Invariance under diffeomorphisms 277
2.2 Pseudo differential operators on manifolds with conical exits . 282
3 Examples and Remarks 287
3.1 Operator valued symbols for boundary value problems 287
3.2 Edge pseudo differential operators 292
References 297
10 Contents
Operator Algebras Associated with Resurgent Transforms and Differ¬
ential Equations on Manifolds with Singularities 300
B. W. Schulze, B. Sternin, and V. Shatalov
Introduction 300
1 General theory 301
1.1 Preliminaries 301
1.2 Function spaces 303
Resurgent representations 303
Function space scales 306
1.3 Spaces with asymptotics 307
Preliminary considerations 307
Main definitions 308
Elements with simple singularities 311
1.4 Operator algebras 312
Description of generators 312
Functions of generators 313
Construction of the operator algebras 315
Ellipticity and regularizes 317
2 Applications: Differential equations on manifolds with cuspidal points 319
2.1 Finiteness theorem 319
Statement of the problem 320
Construction of local regularizers 322
The global regularizer and the Fredholm property 323
2.2 Deformation of resurgent transforms 324
Definition of the deformation 324
Deformation of the operators and the index theorem 327
2.3 Equations in spaces with asymptotics 329
Statement of the problem 329
Notes on the methods 330
References 331
Nonstationary Problems for Borel Fuchs Type Equations 334
B. W. Schulze, B. Sternin, and V. Shatalov
Introduction 334
1 Solution of the problem in small 336
1.1 Degeneration of first degree 337
1.2 Degeneration of higher degree 342
2 Solution of the problem in large 348
2.1 Degeneration of first degree 349
2.2 Degeneration of higher degree 353
3 Investigation of nonstationary problems in abstract algebras 355
3.1 General theory 355
3.2 Example 361
Contents IX
References 364
List of Authors 365
|
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| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011534743 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:11:23Z |
| institution | BVB |
| isbn | 3055017765 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007763861 |
| oclc_num | 39351174 |
| open_access_boolean | |
| owner | DE-703 DE-355 DE-BY-UBR DE-521 DE-634 DE-11 |
| owner_facet | DE-703 DE-355 DE-BY-UBR DE-521 DE-634 DE-11 |
| physical | 366 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Akad.-Verl. |
| record_format | marc |
| series | Mathematical topics |
| series2 | Mathematical topics |
| spelling | Spectral theory, microlocal analysis, singular manifolds ed. by Michael Demuth ... Berlin Akad.-Verl. 1997 366 S. txt rdacontent n rdamedia nc rdacarrier Mathematical topics 14 : Advances in partial differential equations Analyse microlocale Analyse microlocale ram Calcul pseudo-différentiel Capacité Diffusion (physique nucléaire) ram Equation type Borel-Fuchs Espace Dirichlet Fonctions résurgentes ram Opérateurs intégraux ram Spectre (Mathématiques) Théorie spectrale (mathématiques) ram Variété singulière Microlocal analysis Spectral theory (Mathematics) Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd rswk-swf Kapazität Mathematik (DE-588)4163239-4 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Soliton (DE-588)4135213-0 gnd rswk-swf Partieller Differentialoperator (DE-588)4173439-7 gnd rswk-swf Singularität Mathematik (DE-588)4077459-4 gnd rswk-swf Asymptotisches Lösungsverhalten (DE-588)4134367-0 gnd rswk-swf Regularität (DE-588)4049074-9 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Mikrolokale Analysis (DE-588)4169832-0 gnd rswk-swf Fourier-Integraloperator (DE-588)4155104-7 gnd rswk-swf Partieller Differentialoperator (DE-588)4173439-7 s Spektraltheorie (DE-588)4116561-5 s Kapazität Mathematik (DE-588)4163239-4 s Mikrolokale Analysis (DE-588)4169832-0 s DE-604 Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 s Soliton (DE-588)4135213-0 s Fourier-Integraloperator (DE-588)4155104-7 s Mannigfaltigkeit (DE-588)4037379-4 s Singularität Mathematik (DE-588)4077459-4 s Partielle Differentialgleichung (DE-588)4044779-0 s Asymptotisches Lösungsverhalten (DE-588)4134367-0 s Regularität (DE-588)4049074-9 s Demuth, Michael 1946- Sonstige (DE-588)130367478 oth Mathematical topics 14 : Advances in partial differential equations (DE-604)BV008671507 14 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007763861&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Spectral theory, microlocal analysis, singular manifolds Mathematical topics Analyse microlocale Analyse microlocale ram Calcul pseudo-différentiel Capacité Diffusion (physique nucléaire) ram Equation type Borel-Fuchs Espace Dirichlet Fonctions résurgentes ram Opérateurs intégraux ram Spectre (Mathématiques) Théorie spectrale (mathématiques) ram Variété singulière Microlocal analysis Spectral theory (Mathematics) Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd Kapazität Mathematik (DE-588)4163239-4 gnd Spektraltheorie (DE-588)4116561-5 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Soliton (DE-588)4135213-0 gnd Partieller Differentialoperator (DE-588)4173439-7 gnd Singularität Mathematik (DE-588)4077459-4 gnd Asymptotisches Lösungsverhalten (DE-588)4134367-0 gnd Regularität (DE-588)4049074-9 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Mikrolokale Analysis (DE-588)4169832-0 gnd Fourier-Integraloperator (DE-588)4155104-7 gnd |
| subject_GND | (DE-588)4278277-6 (DE-588)4163239-4 (DE-588)4116561-5 (DE-588)4044779-0 (DE-588)4135213-0 (DE-588)4173439-7 (DE-588)4077459-4 (DE-588)4134367-0 (DE-588)4049074-9 (DE-588)4037379-4 (DE-588)4169832-0 (DE-588)4155104-7 |
| title | Spectral theory, microlocal analysis, singular manifolds |
| title_auth | Spectral theory, microlocal analysis, singular manifolds |
| title_exact_search | Spectral theory, microlocal analysis, singular manifolds |
| title_full | Spectral theory, microlocal analysis, singular manifolds ed. by Michael Demuth ... |
| title_fullStr | Spectral theory, microlocal analysis, singular manifolds ed. by Michael Demuth ... |
| title_full_unstemmed | Spectral theory, microlocal analysis, singular manifolds ed. by Michael Demuth ... |
| title_short | Spectral theory, microlocal analysis, singular manifolds |
| title_sort | spectral theory microlocal analysis singular manifolds |
| topic | Analyse microlocale Analyse microlocale ram Calcul pseudo-différentiel Capacité Diffusion (physique nucléaire) ram Equation type Borel-Fuchs Espace Dirichlet Fonctions résurgentes ram Opérateurs intégraux ram Spectre (Mathématiques) Théorie spectrale (mathématiques) ram Variété singulière Microlocal analysis Spectral theory (Mathematics) Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd Kapazität Mathematik (DE-588)4163239-4 gnd Spektraltheorie (DE-588)4116561-5 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Soliton (DE-588)4135213-0 gnd Partieller Differentialoperator (DE-588)4173439-7 gnd Singularität Mathematik (DE-588)4077459-4 gnd Asymptotisches Lösungsverhalten (DE-588)4134367-0 gnd Regularität (DE-588)4049074-9 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Mikrolokale Analysis (DE-588)4169832-0 gnd Fourier-Integraloperator (DE-588)4155104-7 gnd |
| topic_facet | Analyse microlocale Calcul pseudo-différentiel Capacité Diffusion (physique nucléaire) Equation type Borel-Fuchs Espace Dirichlet Fonctions résurgentes Opérateurs intégraux Spectre (Mathématiques) Théorie spectrale (mathématiques) Variété singulière Microlocal analysis Spectral theory (Mathematics) Nichtlineare Schrödinger-Gleichung Kapazität Mathematik Spektraltheorie Partielle Differentialgleichung Soliton Partieller Differentialoperator Singularität Mathematik Asymptotisches Lösungsverhalten Regularität Mannigfaltigkeit Mikrolokale Analysis Fourier-Integraloperator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007763861&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008671507 |
| work_keys_str_mv | AT demuthmichael spectraltheorymicrolocalanalysissingularmanifolds |