The Ergodic Theory of Lattice Subgroups AM 172 is popular PDF and ePub book, written by Alexander Gorodnik in 2010, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, The Ergodic Theory of Lattice Subgroups AM 172 can be Read Online from any device for your convenience.
The Ergodic Theory of Lattice Subgroups AM 172 Book PDF Summary
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.
Detail Book of The Ergodic Theory of Lattice Subgroups AM 172 PDF
- Author : Alexander Gorodnik
- Release : 01 October 2024
- Publisher : Princeton University Press
- ISBN : 9780691141855
- Genre : Mathematics
- Total Page : 136 pages
- Language : English
- PDF File Size : 18,8 Mb
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