Operator theoretic aspects of ergodic theory:
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| Main Authors: | , , , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cham
Springer
[2015]
|
| Series: | Graduate Texts in Mathematics
272 |
| Subjects: | |
| Online Access: | BTU01 FRO01 TUM01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Physical Description: | 1 Online Ressource (XVIII, 628 Seiten, 25 illus., 1 illus. in color) |
| ISBN: | 9783319168982 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-3-319-16898-2 |
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Record in the Search Index
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| adam_text | OPERATOR THEORETIC ASPECTS OF ERGODIC THEORY
/ EISNER, TANJA
: 2015
TABLE OF CONTENTS / INHALTSVERZEICHNIS
WHAT IS ERGODIC THEORY?
TOPOLOGICAL DYNAMICAL SYSTEMS
MINIMALITY AND RECURRENCE
THEC*-ALGEBRA C(K) AND THE KOOPMAN OPERATOR
MEASURE-PRESERVING SYSTEMS
RECURRENCE AND ERGODICITY
THE BANACH LATTICE LP AND THE KOOPMAN OPERATOR
THE MEAN ERGODIC THEOREM
MIXING DYNAMICAL SYSTEMS
MEAN ERGODIC OPERATORS ON C(K)
THE POINTWISE ERGODIC THEOREM
ISOMORPHISMS AND TOPOLOGICAL MODELS
MARKOV OPERATORS
COMPACT SEMIGROUPS AND GROUPS
TOPOLOGICAL DYNAMICS REVISITED
THE JACOBS–DE LEEUW–GLICKSBERG DECOMPOSITION
DYNAMICAL SYSTEMS WITH DISCRETE SPECTRUM
A GLIMPSE AT ARITHMETIC PROGRESSIONS
JOININGS
THE HOST–KRA– TAO THEOREM
MORE ERGODIC THEOREMS
APPENDIX A: TOPOLOGY
APPENDIXB: MEASURE AND INTEGRATION THEORY.-APPENDIX C: FUNCTIONAL
ANALYSIS
APPENDIX D: THE RIESZ REPRESENTATION THEOREM
APPENDIXE: THEOREMS OF EBERLEIN, GROTHENDIECK, AND ELLIS
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
OPERATOR THEORETIC ASPECTS OF ERGODIC THEORY
/ EISNER, TANJA
: 2015
ABSTRACT / INHALTSTEXT
STUNNING RECENT RESULTS BY HOST–KRA, GREEN–TAO, AND OTHERS,
HIGHLIGHT THE TIMELINESS OF THIS SYSTEMATIC INTRODUCTION TO CLASSICAL
ERGODIC THEORY USING THE TOOLS OF OPERATOR THEORY. ASSUMING NO PRIOR
EXPOSURE TO ERGODIC THEORY, THIS BOOK PROVIDES A MODERN FOUNDATION FOR
INTRODUCTORY COURSES ON ERGODIC THEORY, ESPECIALLY FOR STUDENTS OR
RESEARCHERS WITH AN INTEREST IN FUNCTIONAL ANALYSIS. WHILE BASIC
ANALYTIC NOTIONS AND RESULTS ARE REVIEWED IN SEVERAL APPENDICES, MORE
ADVANCED OPERATOR THEORETIC TOPICS ARE DEVELOPED IN DETAIL, EVEN BEYOND
THEIR IMMEDIATE CONNECTION WITH ERGODIC THEORY. AS A CONSEQUENCE, THE
BOOK IS ALSO SUITABLE FOR ADVANCED OR SPECIAL-TOPIC COURSES ON
FUNCTIONAL ANALYSIS WITH APPLICATIONS TO ERGODIC THEORY. TOPICS INCLUDE:
•AN INTUITIVE INTRODUCTION TO ERGODIC THEORY •AN INTRODUCTION TO THE
BASIC NOTIONS, CONSTRUCTIONS, AND STANDARD EXAMPLES OF TOPOLOGICAL
DYNAMICAL SYSTEMS •KOOPMAN OPERATORS, BANACH LATTICES, LATTICE AND
ALGEBRA HOMOMORPHISMS, AND THE GELFAND–NAIMARK THEOREM
•MEASURE-PRESERVING DYNAMICAL SYSTEMS •VON NEUMANN’S MEAN ERGODIC
THEOREM AND BIRKHOFF’S POINTWISE ERGODIC THEOREM •STRONGLY AND
WEAKLY MIXING SYSTEMS •AN EXAMINATION OF NOTIONS OF ISOMORPHISM FOR
MEASURE-PRESERVING SYSTEMS •MARKOV OPERATORS, AND THE RELATED CONCEPT
OF A FACTOR OF A MEASURE-PRESERVING SYSTEM •COMPACT GROUPS AND
SEMIGROUPS, AND A POWERFUL TOOL IN THEIR STUDY, THE JACOBS–DE
LEEUW–GLICKSBERG DECOMPOSITION •AN INTRODUCTION TO THE SPECTRAL
THEORY OF DYNAMICAL SYSTEMS, THE THEOREMS OF FURSTENBERG AND WEISS ON
MULTIPLE RECURRENCE, AND APPLICATIONS OF DYNAMICAL SYSTEMS TO
COMBINATORICS (THEOREMS OF VAN DER WAERDEN, GALLAI, AND HINDMAN,
FURSTENBERG’S CORRESPONDENCE PRINCIPLE, THEOREMS OF ROTH AND
FURSTENBERG–SARKOEZY) BEYOND ITS USE IN THE CLASSROOM, OPERATOR
THEORETIC ASPECTS OF ERGODIC THEORY CAN SERVE AS A VALUABLE FOUNDATION
FOR DOING RESEARCH AT THE INTERSECTION OF ERGODIC THEORY AND OPERATOR
THEORY
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Eisner, Tatjana 1980- Farkas, Bálint Haase, Markus 1970- Nagel, Rainer 1940- |
| author_GND | (DE-588)133328031 (DE-588)1060737418 (DE-588)141517956 |
| author_facet | Eisner, Tatjana 1980- Farkas, Bálint Haase, Markus 1970- Nagel, Rainer 1940- |
| author_role | aut aut aut aut |
| author_sort | Eisner, Tatjana 1980- |
| author_variant | t e te b f bf m h mh r n rn |
| building | Verbundindex |
| bvnumber | BV043209734 |
| classification_rvk | SK 620 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA |
| ctrlnum | (OCoLC)932039164 (DE-599)BVBBV043209734 |
| dewey-full | 515.48 515.39 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.48 515.39 |
| dewey-search | 515.48 515.39 |
| dewey-sort | 3515.48 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-319-16898-2 |
| format | Electronic eBook |
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| id | DE-604.BV043209734 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:20:36Z |
| institution | BVB |
| isbn | 9783319168982 |
| issn | 0072-5285 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028632894 |
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| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Springer |
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| series | Graduate Texts in Mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Eisner, Tatjana 1980- Verfasser (DE-588)133328031 aut Operator theoretic aspects of ergodic theory Tanja Eisner, Bálint Farkas, Markus Haase, Rainer Nagel Cham Springer [2015] © 2015 1 Online Ressource (XVIII, 628 Seiten, 25 illus., 1 illus. in color) txt rdacontent c rdamedia cr rdacarrier Graduate texts in mathematics 272 0072-5285 Mathematics Dynamics Ergodic theory Functional analysis Operator theory Dynamical Systems and Ergodic Theory Operator Theory Functional Analysis Mathematik Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Operatortheorie (DE-588)4075665-8 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 s Operatortheorie (DE-588)4075665-8 s DE-604 Farkas, Bálint Verfasser aut Haase, Markus 1970- Verfasser (DE-588)1060737418 aut Nagel, Rainer 1940- Verfasser (DE-588)141517956 aut Erscheint auch als Druckausgabe 978-3-319-16897-5 Graduate Texts in Mathematics 272 (DE-604)BV035421258 272 https://doi.org/10.1007/978-3-319-16898-2 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028632894&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028632894&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Eisner, Tatjana 1980- Farkas, Bálint Haase, Markus 1970- Nagel, Rainer 1940- Operator theoretic aspects of ergodic theory Graduate Texts in Mathematics Mathematics Dynamics Ergodic theory Functional analysis Operator theory Dynamical Systems and Ergodic Theory Operator Theory Functional Analysis Mathematik Ergodentheorie (DE-588)4015246-7 gnd Operatortheorie (DE-588)4075665-8 gnd |
| subject_GND | (DE-588)4015246-7 (DE-588)4075665-8 |
| title | Operator theoretic aspects of ergodic theory |
| title_auth | Operator theoretic aspects of ergodic theory |
| title_exact_search | Operator theoretic aspects of ergodic theory |
| title_full | Operator theoretic aspects of ergodic theory Tanja Eisner, Bálint Farkas, Markus Haase, Rainer Nagel |
| title_fullStr | Operator theoretic aspects of ergodic theory Tanja Eisner, Bálint Farkas, Markus Haase, Rainer Nagel |
| title_full_unstemmed | Operator theoretic aspects of ergodic theory Tanja Eisner, Bálint Farkas, Markus Haase, Rainer Nagel |
| title_short | Operator theoretic aspects of ergodic theory |
| title_sort | operator theoretic aspects of ergodic theory |
| topic | Mathematics Dynamics Ergodic theory Functional analysis Operator theory Dynamical Systems and Ergodic Theory Operator Theory Functional Analysis Mathematik Ergodentheorie (DE-588)4015246-7 gnd Operatortheorie (DE-588)4075665-8 gnd |
| topic_facet | Mathematics Dynamics Ergodic theory Functional analysis Operator theory Dynamical Systems and Ergodic Theory Operator Theory Functional Analysis Mathematik Ergodentheorie Operatortheorie |
| url | https://doi.org/10.1007/978-3-319-16898-2 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028632894&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028632894&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035421258 |
| work_keys_str_mv | AT eisnertatjana operatortheoreticaspectsofergodictheory AT farkasbalint operatortheoreticaspectsofergodictheory AT haasemarkus operatortheoreticaspectsofergodictheory AT nagelrainer operatortheoreticaspectsofergodictheory |