Evolution equations, Feshbach resonances, singular Hodge theory:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin [u.a.]
Wiley-VCH
1999
|
| Edition: | 1. ed. |
| Series: | Mathematical topics
16 :Advances in partial differential equations |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 431 S. |
| ISBN: | 3527402330 |
Staff View
MARC
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| 245 | 1 | 0 | |a Evolution equations, Feshbach resonances, singular Hodge theory |c ed. by Michael Demuth ... |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Wiley-VCH |c 1999 | |
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Record in the Search Index
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| adam_text | Contents
Singular Interaction Problems of Parabolic Type with Distribution and
Hyperfunction Data 11
G. Lumer
1 Introduction 11
2 Notations, terminology, recalling known facts.
Basic initial context 13
3 Regular problems with variable boundary values 14
4 A first example of asymptotic approach leading up to a singular inter¬
action: heat explosions 16
5 General transition/interaction problems with distribution data, in pa¬
rabolic context 20
6 General transition/interaction problems with hyperfunction data, in
parabolic context 25
7 Transitions and interactions in the presence of positivity 28
8 The full implications of positivity 30
9 Transition/interaction problems in classical context 32
10 True hyperfunction data and open questions 34
References 35
Asymptotic Laplace Transforms and Evolution Equations 37
G. Lumer, F. Neubrander
1 Introduction 37
2 Asymptotic Laplace Transforms 38
3 The Abstract Cauchy Problem 51
References 56
8 Contents
Local Operator Methods and Time Dependent Parabolic Equations on
Non Cylindrical Domains 58
G. Lumer, R. Schnaubelt
1 Introduction and general information 59
1.1 Introduction 59
1.2 List of hypotheses and definitions 61
1.3 List of symbols and notation 62
2 Local operators in general and parabolic local operators 62
2.1 Basic notations, closure and completion of local operators ... 62
2.2 Parabolic extension of local operators in space time 69
2.3 Maximum principles for parabolic local operators 74
3 Localization and well posedness of Cauchy problems 78
3.1 Introduction 78
3.2 Excessive barriers and approximate solutions 81
3.3 Spatial parabolic extension 85
3.4 Local Feller semigroups 88
3.5 Cauchy barriers and well posedness of Cauchy problems .... 91
4 Time dependent parabolic problems on non cylindrical domains .... 96
4.1 Introduction 96
4.2 Parabolic operators and space time semigroups 98
4.3 Well posedness of parabolic problems on non cylindrical domains 103
4.4 Parabolic and standard parabolic problems Ill
5 Semilinear parabolic problems on non cylindrical domains 113
6 Applications 116
6.1 Parabolic partial differential equations of second order 116
6.2 Diffusion problems on networks 123
References 126
Tunneling Effects for /i Pseudodifferential Operators, Feshbach Reso¬
nances, and the Born Oppenheimer Approximation 131
M. Rouleux
Introduction 132
1 Preliminaries and reduction of V near a branching point 143
2 The model of branching 158
3 Normalization 164
4 The WKB constructions 170
5 The Grusin problem 193
6 The Fredholm alternative for V 197
7 The width of resonances 204
8 The Born Oppenheimer approximation 215
Appendix 221
References 237
Contents 9
The Conjugate Operator Method: Application to Dirac Operators and
to Stratified Media 243
A. Boutet de Monvel, R. Purice
1 Introduction 243
2 The Abstract Method 247
2.1 Relative Smoothness 247
2.2 The Conjugate Operator 248
2.3 The Differential Inequality 250
2.4 Regularity with respect to an automorphism group 255
2.5 The Limiting Absorption Principle in Besov Spaces 257
2.6 Self adjoint Operators with Spectral Gap 259
2.7 Existence and Completeness of Wave Operators 260
3 Applications of the conjugate operator method 261
3.1 Introduction 261
3.2 Pseudo Differential Operators 263
3.3 Singular Second Order Elliptic Operators 265
3.4 N Body Hamiltonians 267
3.5 Hamiltonians with Magnetic Fields 270
3.6 Dirac Hamiltonians 273
3.7 Wave Propagation in Inhomogeneous Media 276
4 References 283
Elliptic Complexes of Pseudodifferential Operators on Manifolds with
Edges 287
B. W. Schulze, N. Tarkhanov
Introduction 287
1 Manifolds with Edges 290
1.1 C°° structures 290
1.2 Vector bundles 293
1.3 Blowing up edges 297
1.4 Distributions on manifolds with edges 299
2 Sobolev Spaces with Asymptotics 300
2.1 Twisted Sobolev spaces 300
2.2 Sobolev spaces on manifolds with edges 303
2.3 The nature of asymptotics 306
2.4 Invariance 310
3 Operator Algebras on a Manifold with Edges 316
3.1 Typical symbols 317
3.2 Quantisation 325
3.3 Green operators 334
3.4 The operator algebra 342
4 Elliptic Edge Problems 349
4.1 The concept of ellipticity 349
10 Contents
4.2 Parametrix construction 362
4.3 Fredholm property 375
4.4 Reductions of orders 381
5 Complexes over a Manifold with Edges 393
5.1 Fredholm quasicomplexes 394
5.2 Elliptic quasicomplexes 404
5.3 Hodge theory 413
5.4 External multiplication 417
Bibliography 426
List of Authors 432
|
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| indexdate | 2024-07-09T18:26:23Z |
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| isbn | 3527402330 |
| language | English |
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| physical | 431 S. |
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| publisher | Wiley-VCH |
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| series | Mathematical topics |
| series2 | Mathematical topics |
| spelling | Evolution equations, Feshbach resonances, singular Hodge theory ed. by Michael Demuth ... 1. ed. Berlin [u.a.] Wiley-VCH 1999 431 S. txt rdacontent n rdamedia nc rdacarrier Mathematical topics 16 :Advances in partial differential equations Differential equations, Partial Equations aux dérivées partielles - Solutions numériques ram Equations d'évolution ram Hodge, Théorie de ram Pseudodifferential operators Differential equations, Partial Numerical solutions Evolution equations Hodge theory Elliptischer Komplex (DE-588)4540443-4 gnd rswk-swf Pseudodifferentialoperator (DE-588)4047640-6 gnd rswk-swf Konjugierter Operator (DE-588)4540442-2 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 gnd rswk-swf Hodge-Theorie (DE-588)4135967-7 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Pseudodifferentialoperator (DE-588)4047640-6 s Elliptischer Komplex (DE-588)4540443-4 s Hodge-Theorie (DE-588)4135967-7 s DE-604 Konjugierter Operator (DE-588)4540442-2 s Spektraltheorie (DE-588)4116561-5 s Evolutionsgleichung (DE-588)4129061-6 s Demuth, Michael 1946- Sonstige (DE-588)130367478 oth Mathematical topics 16 :Advances in partial differential equations (DE-604)BV008671507 16 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008389425&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Evolution equations, Feshbach resonances, singular Hodge theory Mathematical topics Differential equations, Partial Equations aux dérivées partielles - Solutions numériques ram Equations d'évolution ram Hodge, Théorie de ram Pseudodifferential operators Differential equations, Partial Numerical solutions Evolution equations Hodge theory Elliptischer Komplex (DE-588)4540443-4 gnd Pseudodifferentialoperator (DE-588)4047640-6 gnd Konjugierter Operator (DE-588)4540442-2 gnd Evolutionsgleichung (DE-588)4129061-6 gnd Hodge-Theorie (DE-588)4135967-7 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| subject_GND | (DE-588)4540443-4 (DE-588)4047640-6 (DE-588)4540442-2 (DE-588)4129061-6 (DE-588)4135967-7 (DE-588)4116561-5 |
| title | Evolution equations, Feshbach resonances, singular Hodge theory |
| title_auth | Evolution equations, Feshbach resonances, singular Hodge theory |
| title_exact_search | Evolution equations, Feshbach resonances, singular Hodge theory |
| title_full | Evolution equations, Feshbach resonances, singular Hodge theory ed. by Michael Demuth ... |
| title_fullStr | Evolution equations, Feshbach resonances, singular Hodge theory ed. by Michael Demuth ... |
| title_full_unstemmed | Evolution equations, Feshbach resonances, singular Hodge theory ed. by Michael Demuth ... |
| title_short | Evolution equations, Feshbach resonances, singular Hodge theory |
| title_sort | evolution equations feshbach resonances singular hodge theory |
| topic | Differential equations, Partial Equations aux dérivées partielles - Solutions numériques ram Equations d'évolution ram Hodge, Théorie de ram Pseudodifferential operators Differential equations, Partial Numerical solutions Evolution equations Hodge theory Elliptischer Komplex (DE-588)4540443-4 gnd Pseudodifferentialoperator (DE-588)4047640-6 gnd Konjugierter Operator (DE-588)4540442-2 gnd Evolutionsgleichung (DE-588)4129061-6 gnd Hodge-Theorie (DE-588)4135967-7 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| topic_facet | Differential equations, Partial Equations aux dérivées partielles - Solutions numériques Equations d'évolution Hodge, Théorie de Pseudodifferential operators Differential equations, Partial Numerical solutions Evolution equations Hodge theory Elliptischer Komplex Pseudodifferentialoperator Konjugierter Operator Evolutionsgleichung Hodge-Theorie Spektraltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008389425&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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