Ergodic averages on spheres

DOI10.1007/BF02788837zbMath0828.28007MaRDI QIDQ1317275

Roger L. Jones

Publication date: 4 January 1996

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

zbMATH Keywords

commuting ergodic invertible measure-preserving flowsergodic averaging operator

Mathematics Subject Classification ID

Ergodic theory of linear operators (47A35) One-parameter continuous families of measure-preserving transformations (28D10)

Related Items

A generalization of Birkhoff's pointwise ergodic theorem ⋮ Pointwise ergodic theorems for radial averages on simple Lie groups. I ⋮ Ergodic averages on circles ⋮ Pointwise ergodic theorems for radial averages on the Heisenberg group ⋮ Weak ergodic averages over dilated measures ⋮ Strong variational and jump inequalities in harmonic analysis ⋮ Pointwise ergodic theorems for radial averages on simple Lie groups. II ⋮ Averages on annuli of Euclidean space ⋮ Quantitative ergodic theorems and their number-theoretic applications ⋮ Harmonic Analysis and Pointwise Ergodic Theorems for Noncommuting Transformations ⋮ Non-commutative ergodic averages of balls and spheres over Euclidean spaces ⋮ Spherical means, wave equations, and Hermite-Laguerre expansions ⋮ The spherical ergodic theorem revisited ⋮ Spectral criteria, SLLN's and a.s. convergence of series of stationary variables ⋮ A sparse equidistribution result for $(\operatorname {SL}(2,\mathbb {R})/\Gamma _0)^{n}$

Cites Work

• Averages in the plane over convex curves and maximal operators
• Locally compact measure preservng flows
• Counterexamples in ergodic theory and number theory
• Maximal functions: Spherical means
• Problems in harmonic analysis related to curvature
• ERGODIC THEORY AND TRANSLATION-INVARIANT OPERATORS
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