Mathematical foundations of the state lumping of large systems:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch Russisch |
| Veröffentlicht: |
Dordrecht u.a.
Kluwer Acad. Publ.
1993
|
| Schriftenreihe: | Mathematics and its applications
264 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005441147&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Aus dem Russ. übers. |
| Umfang: | X, 278 S. graph. Darst. |
| ISBN: | 0792324137 |
Internformat
MARC
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| 240 | 1 | 0 | |a Matematičeskie osnovy fazovogo ukrupnenija složnych sistem |
| 245 | 1 | 0 | |a Mathematical foundations of the state lumping of large systems |c by Vladimir S. Korolyuk and Anatoly F. Turbin |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. Publ. |c 1993 | |
| 300 | |a X, 278 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Mathematics and its applications |v 264 | |
| 500 | |a Aus dem Russ. übers. | ||
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| 650 | 7 | |a Perturbation (Mathématiques) |2 ram | |
| 650 | 4 | |a Linear operators | |
| 650 | 4 | |a Markov processes | |
| 650 | 4 | |a Perturbation (Mathematics) | |
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Datensatz im Suchindex
| _version_ | 1819347303062831104 |
|---|---|
| adam_text | CONTENTS
Introduction vii
Chapter 1. Classes of Linear Operators 1
1.1. Basic notions 1
1.2. Closed and closable operators 4
1.3. Normally solvable operators 12
1.4. Invertibly reducible operators 18
1.5. Pseudo resolvents 29
Chapter 2. Semigroups of Operators and Markov Processes 33
2.1. Basic notions 33
2.2. Infinitesimal operators of ergodic Markov processes 35
2.3. Holomorphic semigroups with invertibly reducible infinitesimal
operators 43
2.4. Semigroups of operators uniformly and strongly ergodic at the infinity 46
2.5. Generating operators of ergodic semi Markov processes 53
2.6. Abstract potential operators 57
2.7. Examples of invertibly reducible operators 65
Chapter 3. Perturbations of Invertibly Reducible Operators 81
3.1. Eigen projectors and eigen operators 81
3.2. Inversion of an invertibly reducible operator perturbed on the spectrum 90
3.3. Resolvents of singularly perturbed semigroups 98
3.4. Limit theorems and asymptotic expansions for resolvents of singularly
perturbed semigroups 103
3.5. Limit theorems and asymptotic expansions for resolvents of singularly
perturbed semigroups. The case of s 2 109
v
vi Contents
Chapter 4. Singular Perturbations of Holomorphic Semigroups 119
4.1. Principal problems. The method of Vishyk Lyusternik Vasilyeva 119
4.2. Structure of singularly perturbed semigroups 121
4.3. Regular lumped approximations to solutions of singularly perturbed
equations 127
Chapter 5. Asymptotic Expansions and Limit Theorems 131
5.1. Strong limits of singularly perturbed semigroups. Resolvent approach 131
5.2. Asymptotic analysis of singularly perturbed semigroups. The case of
s= 134
5.3. Asymptotic analysis of singularly perturbed semigroups 153
Chapter 6. Asymptotic Phase Lumping of Markov and Semi
Markov Processes 167
6.1. Limit theorems 167
6.2. Asymptotic phase lumping. The case of s=l 181
6.3. Some examples 198
6.4. Asymptotic phase lumping. The case of s 2 202
6.5. Classification of processes admitting asymptotic phase lumping 213
6.6. Limit theorems and asymptotic theorems for additive functionals 214
Chapter 7. Applications of the Theory of Singularly Perturbed
Semigroups 241
7.1. Tikhonov systems of differential equations 241
7.2. Nonrelativistic limit of the Dirac operator 246
7.3. Hydrodynamic limit for the linearized Boltzmann equation 254
References 267
Subject Index 277
|
| any_adam_object | 1 |
| author | Koroljuk, Volodymyr S. 1925- Turbin, Anatolij F. |
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| author_sort | Koroljuk, Volodymyr S. 1925- |
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| dewey-full | 515/.7246 |
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| dewey-sort | 3515 47246 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV008241734 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T09:18:58Z |
| institution | BVB |
| isbn | 0792324137 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005441147 |
| oclc_num | 28293507 |
| open_access_boolean | |
| owner | DE-12 DE-739 DE-188 |
| owner_facet | DE-12 DE-739 DE-188 |
| physical | X, 278 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spellingShingle | Koroljuk, Volodymyr S. 1925- Turbin, Anatolij F. Mathematical foundations of the state lumping of large systems Mathematics and its applications Markov, processus de ram Opérateurs linéaires ram Perturbation (Mathématiques) ram Linear operators Markov processes Perturbation (Mathematics) Großes System (DE-588)4022184-2 gnd Transformation (DE-588)4451062-7 gnd Evolutionsgleichung (DE-588)4129061-6 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Phasenraum (DE-588)4139912-2 gnd |
| subject_GND | (DE-588)4022184-2 (DE-588)4451062-7 (DE-588)4129061-6 (DE-588)4057630-9 (DE-588)4139912-2 |
| title | Mathematical foundations of the state lumping of large systems |
| title_alt | Matematičeskie osnovy fazovogo ukrupnenija složnych sistem |
| title_auth | Mathematical foundations of the state lumping of large systems |
| title_exact_search | Mathematical foundations of the state lumping of large systems |
| title_full | Mathematical foundations of the state lumping of large systems by Vladimir S. Korolyuk and Anatoly F. Turbin |
| title_fullStr | Mathematical foundations of the state lumping of large systems by Vladimir S. Korolyuk and Anatoly F. Turbin |
| title_full_unstemmed | Mathematical foundations of the state lumping of large systems by Vladimir S. Korolyuk and Anatoly F. Turbin |
| title_short | Mathematical foundations of the state lumping of large systems |
| title_sort | mathematical foundations of the state lumping of large systems |
| topic | Markov, processus de ram Opérateurs linéaires ram Perturbation (Mathématiques) ram Linear operators Markov processes Perturbation (Mathematics) Großes System (DE-588)4022184-2 gnd Transformation (DE-588)4451062-7 gnd Evolutionsgleichung (DE-588)4129061-6 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Phasenraum (DE-588)4139912-2 gnd |
| topic_facet | Markov, processus de Opérateurs linéaires Perturbation (Mathématiques) Linear operators Markov processes Perturbation (Mathematics) Großes System Transformation Evolutionsgleichung Stochastischer Prozess Phasenraum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005441147&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
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