The ergodic theory of Lattice subgroups:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Princeton, N.J.
Princeton University Press
[2010]
|
| Schriftenreihe: | Annals of Mathematics Studies
number 172 |
| Links: | https://doi.org/10.1515/9781400831067?locatt=mode:legacy http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400831067&searchTitles=true |
| Beschreibung: | Main description: The results established in this book constitute a new departure in ergodic theory and a significant expansion of its scope. Traditional ergodic theorems focused on amenable groups, and relied on the existence of an asymptotically invariant sequence in the group, the resulting maximal inequalities based on covering arguments, and the transference principle. Here, Alexander Gorodnik and Amos Nevo develop a systematic general approach to the proof of ergodic theorems for a large class of non-amenable locally compact groups and their lattice subgroups. Simple general conditions on the spectral theory of the group and the regularity of the averaging sets are formulated, which suffice to guarantee convergence to the ergodic mean. In particular, this approach gives a complete solution to the problem of establishing mean and pointwise ergodic theorems for the natural averages on semisimple algebraic groups and on their discrete lattice subgroups. Furthermore, an explicit quantitative rate of convergence to the ergodic mean is established in many cases. The topic of this volume lies at the intersection of several mathematical fields of fundamental importance. These include ergodic theory and dynamics of non-amenable groups, harmonic analysis on semisimple algebraic groups and their homogeneous spaces, quantitative non-Euclidean lattice point counting problems and their application to number theory, as well as equidistribution and non-commutative Diophantine approximation. Many examples and applications are provided in the text, demonstrating the usefulness of the results established |
| Umfang: | 1 Online-Ressource (160 S.) |
| ISBN: | 9781400831067 |
| DOI: | 10.1515/9781400831067 |
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| 490 | 1 | |a Annals of Mathematics Studies |v number 172 | |
| 500 | |a Main description: The results established in this book constitute a new departure in ergodic theory and a significant expansion of its scope. Traditional ergodic theorems focused on amenable groups, and relied on the existence of an asymptotically invariant sequence in the group, the resulting maximal inequalities based on covering arguments, and the transference principle. Here, Alexander Gorodnik and Amos Nevo develop a systematic general approach to the proof of ergodic theorems for a large class of non-amenable locally compact groups and their lattice subgroups. Simple general conditions on the spectral theory of the group and the regularity of the averaging sets are formulated, which suffice to guarantee convergence to the ergodic mean. In particular, this approach gives a complete solution to the problem of establishing mean and pointwise ergodic theorems for the natural averages on semisimple algebraic groups and on their discrete lattice subgroups. Furthermore, an explicit quantitative rate of convergence to the ergodic mean is established in many cases. The topic of this volume lies at the intersection of several mathematical fields of fundamental importance. These include ergodic theory and dynamics of non-amenable groups, harmonic analysis on semisimple algebraic groups and their homogeneous spaces, quantitative non-Euclidean lattice point counting problems and their application to number theory, as well as equidistribution and non-commutative Diophantine approximation. Many examples and applications are provided in the text, demonstrating the usefulness of the results established | ||
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| indexdate | 2024-12-20T17:13:29Z |
| institution | BVB |
| isbn | 9781400831067 |
| language | English |
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| publisher | Princeton University Press |
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| spelling | Gorodnik, Alexander 1975- (DE-588)13939463X aut The ergodic theory of Lattice subgroups Princeton, N.J. Princeton University Press [2010] © 2010 1 Online-Ressource (160 S.) txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 172 Main description: The results established in this book constitute a new departure in ergodic theory and a significant expansion of its scope. Traditional ergodic theorems focused on amenable groups, and relied on the existence of an asymptotically invariant sequence in the group, the resulting maximal inequalities based on covering arguments, and the transference principle. Here, Alexander Gorodnik and Amos Nevo develop a systematic general approach to the proof of ergodic theorems for a large class of non-amenable locally compact groups and their lattice subgroups. Simple general conditions on the spectral theory of the group and the regularity of the averaging sets are formulated, which suffice to guarantee convergence to the ergodic mean. In particular, this approach gives a complete solution to the problem of establishing mean and pointwise ergodic theorems for the natural averages on semisimple algebraic groups and on their discrete lattice subgroups. Furthermore, an explicit quantitative rate of convergence to the ergodic mean is established in many cases. The topic of this volume lies at the intersection of several mathematical fields of fundamental importance. These include ergodic theory and dynamics of non-amenable groups, harmonic analysis on semisimple algebraic groups and their homogeneous spaces, quantitative non-Euclidean lattice point counting problems and their application to number theory, as well as equidistribution and non-commutative Diophantine approximation. Many examples and applications are provided in the text, demonstrating the usefulness of the results established Nevo, Amos 1966- (DE-588)139394656 aut Erscheint auch als Druck-Ausgabe 978-0-691-14184-8 Annals of Mathematics Studies number 172 (DE-604)BV040389493 172 https://doi.org/10.1515/9781400831067?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400831067&searchTitles=true Verlag Volltext |
| spellingShingle | Gorodnik, Alexander 1975- Nevo, Amos 1966- The ergodic theory of Lattice subgroups Annals of Mathematics Studies |
| title | The ergodic theory of Lattice subgroups |
| title_auth | The ergodic theory of Lattice subgroups |
| title_exact_search | The ergodic theory of Lattice subgroups |
| title_full | The ergodic theory of Lattice subgroups |
| title_fullStr | The ergodic theory of Lattice subgroups |
| title_full_unstemmed | The ergodic theory of Lattice subgroups |
| title_short | The ergodic theory of Lattice subgroups |
| title_sort | the ergodic theory of lattice subgroups |
| url | https://doi.org/10.1515/9781400831067?locatt=mode:legacy http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400831067&searchTitles=true |
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