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|a 9781400831067
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|a Gorodnik, Alexander
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|a The Ergodic Theory of Lattice Subgroups (AM-172)
|h Elektronische Ressource
|c Alexander Gorodnik, Amos Nevo
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|a Course Book
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|a Princeton, N.J.
|b Princeton University Press
|c [2009]©2009, 2009
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|a online resource 160 pages
|b illustrations
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|a MATHEMATICS / Group Theory
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|a Ergodic theory
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|a Mathematik
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|a Harmonic analysis
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|a Lie groups
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|a Lattice theory
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|a MATHEMATICS / Mathematical Analysis
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|a Mathematics
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|a Probability and Statistics
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|a MATHEMATICS / Calculus
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|a Dynamics
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|a Nevo, Amos
|e [author]
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|a eng
|2 ISO 639-2
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|b GRUYMPG
|a DeGruyter MPG Collection
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|a Annals of Mathematics Studies
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|a Mode of access: Internet via World Wide Web
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|a 10.1515/9781400831067
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|t Princeton eBook Package Backlist 2000-2013
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|t Princeton Univ. Press eBook Package 2000-2013
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|t Princeton eBook Package Backlist 2000-2014
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|t Princeton Annals of Mathematics Backlist eBook Package
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|u https://www.degruyter.com/doi/book/10.1515/9781400831067
|x Verlag
|3 Volltext
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|a 515/.48
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|a 515/.48
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|a 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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