Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators:
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | German |
| Published: |
Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London
Springer
1999
|
| Series: | Lecture notes in mathematics
1718 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 262 S. |
| ISBN: | 3540666281 |
Staff View
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| 100 | 1 | |a Eberle, Andreas |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators |c Andreas Eberle |
| 264 | 1 | |a Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London |b Springer |c 1999 | |
| 300 | |a VIII, 262 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1718 | |
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Record in the Search Index
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| adam_text | Contents
0 Introduction 1
a ) General introduction 1
b ) Results 5
1 Uniqueness problems in various contexts 9
a ) Uniqueness of the martingale problem 10
b ) Cores 17
c ) Essential self adjointness 21
d ) Uniqueness of Dirichlet forms 22
e ) Relations between the notions of uniqueness 24
Appendix
A Existence and uniqueness of C° semigroups on Banach spaces . . 30
B Diffusion operators on Lp spaces 35
2 Lp uniqueness in finite dimensions 41
a ) The regular one dimensional case 42
b ) Examples and counterexamples I : Regular operators 51
1) Diffusion operators on Lp(Rn; dx) 51
2) Operators on LP(RX; e~x^2 dx) 53
3) Perturbations of generalized Schrodinger operators on R1 . . 54
c ) Regular diffusion operators on Rn 55
d ) Examples and counterexamples II : Singular operators 59
1) Singular generalized Schrodinger operators on R1 59
2) Rotationally invariant generalized Schrodinger operators ... 61
3) Degeneracy of second order coefficients 65
e ) The singular one dimensional case 66
f ) Singular diffusion operators on R 75
Appendix
C Regularity of distributional solutions of O.D.E 85
VIII CONTENTS
3 Markov uniqueness 89
a ) Weak Sobolev spaces on Rn and on Banach spaces 92
b ) Weak and strong Sobolev spaces on general state spaces 104
c ) Maximal Dirichlet extensions 112
d ) Markov uniqueness in the one dimensional case 118
e ) Density of smooth functions in weak Sobolev spaces over Rn . . 124
f ) Markov uniqueness in the finite dimensional case 129
g ) Ergodicity and extremality of symmetrizing measures 136
Appendix
D The geometry of diffusion operators 147
1) Generalized differentials 148
2) Measurable co tangent bundles and differentials corresponding
to diffusion operators 149
3) Diffusion operators on manifolds and vector spaces 152
4) Ornstein Uhlenbeck geometries on path and loop spaces ... 153
5) Horizontal and vertical measure valued diffusions 155
6) Divergence operators and symmetrizing measures 159
7) A representation theorem for diffusion operators on L? spaces 162
4 Probabilistic aspects of Lp and Markov uniqueness 169
a ) Feller classification and uniqueness 170
b ) Conservativity, ergodicity, and Markov uniqueness 178
c ) Probabilistic explanations for Lp uniqueness 179
5 First steps in infinite dimensions 185
a ) Infinite dimensional diffusion operators on linear spaces 187
b ) The generator of the Brownian string — A counterexample ... 197
c ) Markov uniqueness of projective limits 215
d ) Approximative approaches to uniqueness and existence in Lp . . 225
e ) Applications to lattice systems in statistical mechanics 234
f ) Stability of LP uniqueness under ff valued perturbations .... 238
1) The general perturbation result 239
2) Perturbations of operators with linear drift 240
3) Infinite dimensional generalized Schrodinger operators .... 245
g ) Applications to perturbed operators 247
1) Finite volume quantum fields 247
2) Perturbations of the Ornstein Uhlenbeck operator 250
3) The Brownian string in a velocity field 251
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| author | Eberle, Andreas |
| author_facet | Eberle, Andreas |
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| author_sort | Eberle, Andreas |
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| discipline | Mathematik |
| format | Thesis Book |
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| indexdate | 2024-07-09T18:34:00Z |
| institution | BVB |
| isbn | 3540666281 |
| language | German |
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| physical | VIII, 262 S. |
| publishDate | 1999 |
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| spelling | Eberle, Andreas Verfasser aut Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators Andreas Eberle Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London Springer 1999 VIII, 262 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1718 Zugl: Bielefeld, Univ., Diss., 1998 Singulärer Differentialoperator (DE-588)4181525-7 gnd rswk-swf Halbgruppe (DE-588)4022990-7 gnd rswk-swf Diffusionsprozess (DE-588)4274463-5 gnd rswk-swf Elliptischer Differentialoperator (DE-588)4140057-4 gnd rswk-swf Eindeutigkeit (DE-588)4151249-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Halbgruppe (DE-588)4022990-7 s Eindeutigkeit (DE-588)4151249-2 s DE-604 Diffusionsprozess (DE-588)4274463-5 s Singulärer Differentialoperator (DE-588)4181525-7 s Elliptischer Differentialoperator (DE-588)4140057-4 s Lecture notes in mathematics 1718 (DE-604)BV000676446 1718 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008710353&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Eberle, Andreas Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators Lecture notes in mathematics Singulärer Differentialoperator (DE-588)4181525-7 gnd Halbgruppe (DE-588)4022990-7 gnd Diffusionsprozess (DE-588)4274463-5 gnd Elliptischer Differentialoperator (DE-588)4140057-4 gnd Eindeutigkeit (DE-588)4151249-2 gnd |
| subject_GND | (DE-588)4181525-7 (DE-588)4022990-7 (DE-588)4274463-5 (DE-588)4140057-4 (DE-588)4151249-2 (DE-588)4113937-9 |
| title | Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators |
| title_auth | Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators |
| title_exact_search | Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators |
| title_full | Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators Andreas Eberle |
| title_fullStr | Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators Andreas Eberle |
| title_full_unstemmed | Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators Andreas Eberle |
| title_short | Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators |
| title_sort | uniqueness and non uniqueness of semigroups generated by singular diffusion operators |
| topic | Singulärer Differentialoperator (DE-588)4181525-7 gnd Halbgruppe (DE-588)4022990-7 gnd Diffusionsprozess (DE-588)4274463-5 gnd Elliptischer Differentialoperator (DE-588)4140057-4 gnd Eindeutigkeit (DE-588)4151249-2 gnd |
| topic_facet | Singulärer Differentialoperator Halbgruppe Diffusionsprozess Elliptischer Differentialoperator Eindeutigkeit Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008710353&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT eberleandreas uniquenessandnonuniquenessofsemigroupsgeneratedbysingulardiffusionoperators |