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The ergodic theory of lattice subgroups [[electronic resource] /] / Alexander Gorodnik and Amos Nevo



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Autore: Gorodnik Alexander <1975-> Visualizza persona
Titolo: The ergodic theory of lattice subgroups [[electronic resource] /] / Alexander Gorodnik and Amos Nevo Visualizza cluster
Pubblicazione: Princeton, N.J., : Princeton University Press, 2009
Edizione: Course Book
Descrizione fisica: 1 online resource (136 p.)
Disciplina: 515/.48
Soggetto topico: Ergodic theory
Lie groups
Lattice theory
Harmonic analysis
Dynamics
Soggetto non controllato: Absolute continuity
Algebraic group
Amenable group
Asymptote
Asymptotic analysis
Asymptotic expansion
Automorphism
Borel set
Bounded function
Bounded operator
Bounded set (topological vector space)
Congruence subgroup
Continuous function
Convergence of random variables
Convolution
Coset
Counting problem (complexity)
Counting
Differentiable function
Dimension (vector space)
Diophantine approximation
Direct integral
Direct product
Discrete group
Embedding
Equidistribution theorem
Ergodic theory
Ergodicity
Estimation
Explicit formulae (L-function)
Family of sets
Haar measure
Hilbert space
Hyperbolic space
Induced representation
Infimum and supremum
Initial condition
Interpolation theorem
Invariance principle (linguistics)
Invariant measure
Irreducible representation
Isometry group
Iwasawa group
Lattice (group)
Lie algebra
Linear algebraic group
Linear space (geometry)
Lipschitz continuity
Mass distribution
Mathematical induction
Maximal compact subgroup
Maximal ergodic theorem
Measure (mathematics)
Mellin transform
Metric space
Monotonic function
Neighbourhood (mathematics)
Normal subgroup
Number theory
One-parameter group
Operator norm
Orthogonal complement
P-adic number
Parametrization
Parity (mathematics)
Pointwise convergence
Pointwise
Principal homogeneous space
Principal series representation
Probability measure
Probability space
Probability
Rate of convergence
Regular representation
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)
Vector group
Vector space
Volume form
Word metric
Classificazione: SI 830
Altri autori: NevoAmos <1966->  
Note generali: Description based upon print version of record.
Nota di bibliografia: Includes bibliographical references and index.
Nota di contenuto: Frontmatter -- Contents -- Preface -- Chapter One. Main results: Semisimple Lie groups case -- Chapter Two. Examples and applications -- Chapter Three. Definitions, preliminaries, and basic tools -- Chapter Four. Main results and an overview of the proofs -- Chapter Five. Proof of ergodic theorems for S-algebraic groups -- Chapter Six. Proof of ergodic theorems for lattice subgroups -- Chapter Seven. Volume estimates and volume regularity -- Chapter Eight. Comments and complements -- Bibliography -- Index
Sommario/riassunto: 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.
Titolo autorizzato: The ergodic theory of lattice subgroups  Visualizza cluster
ISBN: 1-282-30380-5
9786612303807
1-4008-3106-7
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910781200803321
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Serie: Annals of mathematics studies ; ; no. 172.