A01=Alexander Gorodnik
A01=Amos Nevo
Amenable group
Asymptotic analysis
Asymptotic expansion
Author_Alexander Gorodnik
Author_Amos Nevo
Automorphism
Bounded operator
Bounded set (topological vector space)
Category=PBG
Category=PBH
Congruence subgroup
Coset
Counting problem (complexity)
Dimension (vector space)
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equidistribution theorem
Ergodic theory
Estimation
Explicit formulae (L-function)
Family of sets
Haar measure
Hilbert space
Induced representation
Infimum and supremum
Interpolation theorem
Invariant measure
Isometry group
Iwasawa group
Lattice (group)
Lie algebra
Linear algebraic group
Linear space (geometry)
Lipschitz continuity
Mathematical induction
Maximal compact subgroup
Maximal ergodic theorem
Measure (mathematics)
Metric space
Monotonic function
Number theory
One-parameter group
Operator norm
Orthogonal complement
P-adic number
Parity (mathematics)
Pointwise
Pointwise convergence
Principal homogeneous space
Principal series representation
Probability measure
Probability space
Rate of convergence
Representation theory
Resolution of singularities
Sobolev space
Special case
Spectral gap
Spectral method
Spectral theory
Square (algebra)
Subgroup
Subsequence
Subset
Symmetric space
Tensor algebra
Tensor product
Theorem
Transfer principle
Unit sphere
Unit vector
Unitary group
Unitary representation
Upper and lower bounds
Variable (mathematics)
Volume form
Product details
- ISBN 9780691141855
- Weight: 227g
- Dimensions: 152 x 235mm
- Publication Date: 11 Oct 2009
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
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.
