The Ergodic Theory of Lattice Subgroups (AM-172) /

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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 ba...

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Detalles Bibliográficos
Autores principales: Gorodnik, Alexander (Autor), Nevo, Amos (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, NJ : Princeton University Press, [2009]
Edición:Course Book
Colección:Annals of Mathematics Studies ; 172
Temas:
Dynamics.
Ergodic theory.
Harmonic analysis.
Lattice theory.
Lie groups.
MATHEMATICS / Probability & Statistics / General.
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.
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.
Acceso en línea:Texto completo
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Tabla de Contenidos:
  • 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

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