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Alexander Gorodnik - The Ergodic Theory of Lattice Subgroups (AM-172) - 9780691141855 - V9780691141855
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The Ergodic Theory of Lattice Subgroups (AM-172)

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Description for The Ergodic Theory of Lattice Subgroups (AM-172) Paperback. Develops a systematic general approach to the proof of ergodic theorems for a large class of non-amenable locally compact groups and their lattice subgroups. This book formulates simple general conditions on the spectral theory of the group and the regularity of the averaging sets, which suffice to guarantee convergence to the ergodic mean. Series: Annals of Mathematics Studies. Num Pages: 160 pages, 2 line illus. BIC Classification: PBG; PBH. Category: (P) Professional & Vocational; (U) Tertiary Education (US: College). Dimension: 229 x 152 x 13. Weight in Grams: 199.
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.

Product Details

Format
Paperback
Publication date
2009
Publisher
Princeton University Press United States
Number of pages
136
Condition
New
Series
Annals of Mathematics Studies
Number of Pages
160
Place of Publication
New Jersey, United States
ISBN
9780691141855
SKU
V9780691141855
Shipping Time
Usually ships in 7 to 11 working days
Ref
99-1

About Alexander Gorodnik
Alexander Gorodnik is senior research fellow in mathematics at the University of Bristol. Amos Nevo is professor of mathematics at the Technion, Israel Institute for Technology.

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