Ratio limit theorems and applications to ergodic theory

Ryotaro Sato

Displaying similar documents to “Ratio limit theorems and applications to ergodic theory”

On functions with scattered spectra on lea groups

Paweł Głowacki (1981)

Studia Mathematica

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Pointwise ergodic theorems in Lorentz spaces L(p,q) for null preserving transformations

Ryotaro Sato (1995)

Studia Mathematica

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Let (X,ℱ,µ) be a finite measure space and τ a null preserving transformation on (X,ℱ,µ). Functions in Lorentz spaces L(p,q) associated with the measure μ are considered for pointwise ergodic theorems. Necessary and sufficient conditions are given in order that for any f in L(p,q) the ergodic average $n^{- 1} \sum_{i = 0}^{n - 1} f \circ τ^{i} (x)$ converges almost everywhere to a function f* in $L (p_{1}, q_{1}]$ , where (pq) and $(p_{1}, q_{1}]$ are assumed to be in the set $(r, s) : r = s = 1, o r 1 < r < \infty a n d 1 \leq s \leq \infty, o r r = s = \infty$ . Results due to C. Ryll-Nardzewski, S. Gładysz, and I. Assani and J. Woś are generalized...

Weighted L spaces and pointwise ergodic theorems.

Ryotaro Sato (1995)

Publicacions Matemàtiques

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In this paper we give an operator theoretic version of a recent result of F. J. Martín-Reyes and A. de la Torre concerning the problem of finding necessary and sufficient conditions for a nonsingular point transformation to satisfy the Pointwise Ergodic Theorem in L_p. We consider a positive conservative contraction T on L₁ of a σ-finite measure space (X, F, μ), a fixed function e in L₁ with

Finite generators of ergodic endomorphisms

Zbigniew S. Kowalski (1984)

Colloquium Mathematicae

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Some Open Problems in Ergodic Theory

Donald S. Ornstein (1975)

Publications mathématiques et informatique de Rennes

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An Abelian ergodic theorem

Ryotaro Sato (1977)

Commentationes Mathematicae Universitatis Carolinae

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A note on a mean ergodic theorem

A. Al-Hussaini (1974)

Annales Polonici Mathematici

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Construction of non-constant and ergodic cocycles

Mahesh Nerurkar (2000)

Colloquium Mathematicae

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We construct continuous G-valued cocycles that are not cohomologous to any compact constant via a measurable transfer function, provided the underlying dynamical system is rigid and the range group G satisfies a certain general condition. For more general ergodic aperiodic systems, we also show that the set of continuous ergodic cocycles is residual in the class of all continuous cocycles provided the range group G is a compact connected Lie group. The first construction is based on...