Schrödinger operators, Markov semigroups, wavelet analysis, operator algebras:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin
Akad.-Verl.
1996
|
| Edition: | 1. ed. |
| Series: | Mathematical topics
11 : Advances in partial differential equations |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | 404 S. |
| ISBN: | 3055017102 |
Staff View
MARC
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| 245 | 1 | 0 | |a Schrödinger operators, Markov semigroups, wavelet analysis, operator algebras |c ed. by Michael Demuth ... |
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Record in the Search Index
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| adam_text | Contents
Recent Results and Open Problems on Schrodinger Operators, Laplace
Integrals, and Transfer Operators in Large Dimension 11
B. Helffer
1 Introduction 12
1.1 On the way of a program by M. Kac 12
1.2 Presentation of the mathematical problems 12
1.3 Our main toy models 15
1.4 Contents of the survey 16
2 Problems in statistical mechanics 18
2.1 The Curie-Weiss model 18
2.2 The 1-d Ising model 19
2.3 The 2-d Ising model 21
2.4 A simple quantum model 23
2.5 The Kac model A 25
2.6 The multiexponential model 28
2.7 Comments 30
3 Laplace integrals 31
3.1 From spin models to Laplace integrals 31
3.2 Classical Laplace methods 33
3.3 Laplace integrals in large dimension: the thermodynamic limit 35
Thermodynamic limit 35
Exponential convergence 40
Sketch of the proof of the main Theorem 43
3.4 Around the Maximum Principle 45
3.5 Laplace integrals in large dimension: decay of the correlations 49
3.6 Around Brascamp-Lieb inequalities 54
3.7 FKG inequalities 57
3.8 Laplace integrals in large dimensions: semiclassical aspects . . 59
Contents 7
The formal Laplace s method 59
Formal expansion of the thermodynamic limit 64
Semiclassical expansions for the thermodynamic limit 68
3.9 Other semiclassical aspects 72
4 Universal analysis for the Schrodinger operator 76
4.1 Universal estimate of the splitting 76
4.2 Logconcavity of the first eigenfunction 77
4.3 Thermodynamic limit: existence and speed of convergence ... 80
5 Semiclassical analysis for the Schrodinger operator 85
5.1 Introduction 85
5.2 The thermodynamic limit: semiclassical expansions 85
5.3 Splitting in the semiclassical context 87
5.4 Presentation of the rigorous results in the large dimension semi-
classical case for the (DK) model 92
5.5 The harmonic approximation 98
5.6 WKB approximation in an ^°°-ball 108
5.7 Exponentially weighted estimates for the eigenfunctions .... 114
6 From statistical mechanics to quantum mechanics 124
6.1 Introduction 124
6.2 A link between statistical mechanics and quantum mechanics . 126
6.3 Study of the zero spacing limit 130
6.4 Comparison between exp —1(—A + V) and
exp-fF-expiA-exp-fV 135
Some preliminaries 135
Study of the Kac s operator 136
Study of exp -t{-A + V) 138
Conclusion 138
6.5 Semiclassical computations around the transfer operator .... 139
7 Around the Kac operator 141
7.1 Introduction 141
7.2 The general Maximum Principle of Sjostrand, new examples . . 143
7.3 Around logconcavity and FKG inequalities 145
7.4 The thermodynamic limit for the Kac operator 148
7.5 Estimates on the correlations 149
7.6 Universal lower bound for the splitting for the Kac operator . . 150
7.7 Semiclassical aspects 151
8 Open problems 153
References 155
8 Contents
Some Problems on Markov Semigroups 163
V. A. Liskevich and Yu. A. Semenov
Introduction 163
1 Some preliminaries 165
2 Fundamental properties of symmetric Markov generators 170
3 Perturbations of symmetric Markov semigroups. I 177
4 Non-symmetric Markov generators 183
5 Perturbations of symmetric Markov semigroups. II 190
6 Perturbations of symmetric Markov semigroups by potentials 192
7 (Lp,Z/?)-estimates for the resolvent and the semigroup, their integral
properties and related problems 198
8 Strong and Markov uniqueness 203
References 212
Wavelet Analysis of Partial Differential Operators 218
M. Holschneider
1 Introduction 218
2 Wavelet analysis, the basic formulas 221
2.1 The formulas for wavelet analysis and synthesis 221
2.2 Relation between W and M 222
2.3 The reproducing kernel and the cross kernel 223
3 Wavelet transform of distributions 224
3.1 Wavelet analysis of S0(lRn) 224
3.2 The wavelet synthesis 230
3.3 The inverse wavelet transform 231
3.4 The reproducing kernel equation 233
3.5 The cross kernel 235
3.6 The L2-theory 235
3.7 Wavelet analysis of S (IRn) 237
3.8 Bounded sets in S0(IRn) and 5^(IRn) 238
3.9 Singular support of distributions 240
3.10 Wavelet analysis of S(IRn) 241
3.11 Wavelet analysis over T 242
4 Some Banach spaces 244
4.1 Admissible dual pairs 250
4.2 Spaces of periodic functions 251
4.3 Examples of admissible B(Hn) 252
4.4 A priori estimates 253
4.5 Compact embedding 254
5 More general microlocal classes 256
5.1 A non-Euclidian distance 256
Contents 9
5.2 A family of neighborhoods 258
5.3 More about well separated sets 260
5.4 Cutting the half-space 262
5.5 Microlocal classes 265
5.6 Directional microlocal classes 267
6 Operators in wavelet space 269
6.1 Formal properties 269
6.2 Some a priori estimates 271
7 Operator algebras 273
7.1 Convolution estimates 273
7.2 The highly regular Calderon Zygmund operators (CZO) .... 276
7.3 Fourier multipliers as highly regular CZO 279
7.4 Singular integrals as highly regular CZO 280
7.5 The smoothing operators 282
7.6 The small scale averaging operators 286
8 The algebra of smoothly varying space-scale convolution operators . . 288
8.1 The Toeplitz operators 296
8.2 A simplification 299
8.3 The algebra of local wavelet changing operators 301
9 Relation with some classical operators 304
9.1 The pseudo-differential operators 305
10 Elliptic regularity 308
10.1 Elliptic operators 308
10.2 Directional elliptic regularity in domains with cusps 310
11 The diffeomorphism in wavelet space 311
11.1 The locally linear approximation 314
11.2 Transformation behavior of the directional micro-local classes . 315
12 The essential spectrum of some Fourier integral operators 315
12.1 Definition of the transfer operator 315
12.2 A formula for the essential spectral radius 317
12.3 An abstract formula for pess 318
12.4 The essential spectrum of £ 322
12.5 A more explicit formula for pess(£) 325
12.6 A simpler upper bound 331
12.7 The case A7(Tn) 332
13 Appendix 335
A.I On the modulus of continuity 335
A.2 Inverse theorems for global regularity 337
A.3 The class of Zygmund 340
A.4 Inverse theorems for point-wise regularity 342
References 345
10 Contents
On the Index of Elliptic Operators on a Cone 348
B. V. Fedosov and B.-W. Schulze
Introduction 348
1 Preliminary estimates 350
2 A regularized trace of a product 359
3 An algebraical index 362
4 A topological index 367
5 Example 371
References 372
On Composition Series in Algebras of Pseudodifferential Operators and
in Algebras of Wiener—Hopf Operators 373
B. A. Plamenevskij and V. N. Senichkin
1 Introduction 373
2 Sufficient conditions of the triviality of fields of elementary C*-algebras 376
3 Algebras of Wiener-Hopf operators 380
4 Algebras of pseudodifferential operators 389
References 403
List of Authors 405
|
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| id | DE-604.BV010853803 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:00:01Z |
| institution | BVB |
| isbn | 3055017102 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007255494 |
| oclc_num | 36218312 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-703 DE-824 DE-29T DE-521 DE-634 DE-11 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-703 DE-824 DE-29T DE-521 DE-634 DE-11 DE-188 |
| physical | 404 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
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| publisher | Akad.-Verl. |
| record_format | marc |
| series | Mathematical topics |
| series2 | Mathematical topics |
| spelling | Schrödinger operators, Markov semigroups, wavelet analysis, operator algebras ed. by Michael Demuth ... 1. ed. Berlin Akad.-Verl. 1996 404 S. txt rdacontent n rdamedia nc rdacarrier Mathematical topics 11 : Advances in partial differential equations Literaturangaben Algèbres d'opérateurs ram Intégrale Laplace Ondelettes ram Opérateurs différentiels partiels ram Opérateurs pseudo-différentiels ram Schrödinger, Opérateur de ram Semigroupes ram Wiener-Hopf, Opérateurs de ram Operator algebras Partial differential operators Pseudodifferential operators Schrödinger operator Semigroups Wavelets (Mathematics) Wiener-Hopf operators Operatoralgebra (DE-588)4129366-6 gnd rswk-swf Wavelet (DE-588)4215427-3 gnd rswk-swf Hamilton-Operator (DE-588)4072278-8 gnd rswk-swf Quantendynamische Halbgruppe (DE-588)4193982-7 gnd rswk-swf Hamilton-Operator (DE-588)4072278-8 s DE-604 Quantendynamische Halbgruppe (DE-588)4193982-7 s Wavelet (DE-588)4215427-3 s Operatoralgebra (DE-588)4129366-6 s Demuth, Michael 1946- Sonstige (DE-588)130367478 oth Mathematical topics 11 : Advances in partial differential equations (DE-604)BV008671507 11 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007255494&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schrödinger operators, Markov semigroups, wavelet analysis, operator algebras Mathematical topics Algèbres d'opérateurs ram Intégrale Laplace Ondelettes ram Opérateurs différentiels partiels ram Opérateurs pseudo-différentiels ram Schrödinger, Opérateur de ram Semigroupes ram Wiener-Hopf, Opérateurs de ram Operator algebras Partial differential operators Pseudodifferential operators Schrödinger operator Semigroups Wavelets (Mathematics) Wiener-Hopf operators Operatoralgebra (DE-588)4129366-6 gnd Wavelet (DE-588)4215427-3 gnd Hamilton-Operator (DE-588)4072278-8 gnd Quantendynamische Halbgruppe (DE-588)4193982-7 gnd |
| subject_GND | (DE-588)4129366-6 (DE-588)4215427-3 (DE-588)4072278-8 (DE-588)4193982-7 |
| title | Schrödinger operators, Markov semigroups, wavelet analysis, operator algebras |
| title_auth | Schrödinger operators, Markov semigroups, wavelet analysis, operator algebras |
| title_exact_search | Schrödinger operators, Markov semigroups, wavelet analysis, operator algebras |
| title_full | Schrödinger operators, Markov semigroups, wavelet analysis, operator algebras ed. by Michael Demuth ... |
| title_fullStr | Schrödinger operators, Markov semigroups, wavelet analysis, operator algebras ed. by Michael Demuth ... |
| title_full_unstemmed | Schrödinger operators, Markov semigroups, wavelet analysis, operator algebras ed. by Michael Demuth ... |
| title_short | Schrödinger operators, Markov semigroups, wavelet analysis, operator algebras |
| title_sort | schrodinger operators markov semigroups wavelet analysis operator algebras |
| topic | Algèbres d'opérateurs ram Intégrale Laplace Ondelettes ram Opérateurs différentiels partiels ram Opérateurs pseudo-différentiels ram Schrödinger, Opérateur de ram Semigroupes ram Wiener-Hopf, Opérateurs de ram Operator algebras Partial differential operators Pseudodifferential operators Schrödinger operator Semigroups Wavelets (Mathematics) Wiener-Hopf operators Operatoralgebra (DE-588)4129366-6 gnd Wavelet (DE-588)4215427-3 gnd Hamilton-Operator (DE-588)4072278-8 gnd Quantendynamische Halbgruppe (DE-588)4193982-7 gnd |
| topic_facet | Algèbres d'opérateurs Intégrale Laplace Ondelettes Opérateurs différentiels partiels Opérateurs pseudo-différentiels Schrödinger, Opérateur de Semigroupes Wiener-Hopf, Opérateurs de Operator algebras Partial differential operators Pseudodifferential operators Schrödinger operator Semigroups Wavelets (Mathematics) Wiener-Hopf operators Operatoralgebra Wavelet Hamilton-Operator Quantendynamische Halbgruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007255494&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008671507 |
| work_keys_str_mv | AT demuthmichael schrodingeroperatorsmarkovsemigroupswaveletanalysisoperatoralgebras |