Displaying similar documents to “On general Lipschitzian kernels.”

Spectral properties of ergodic dynamical systems conjugate to their composition squares

Geoffrey R. Goodson (2007)

Colloquium Mathematicae

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Let S and T be automorphisms of a standard Borel probability space. Some ergodic and spectral consequences of the equation ST = T²S are given for T ergodic and also when Tⁿ = I for some n>2. These ideas are used to construct examples of ergodic automorphisms S with oscillating maximal spectral multiplicity function. Other examples illustrating the theory are given, including Gaussian automorphisms having simple spectra and conjugate to their squares.

Operators with an ergodic power

Teresa Bermúdez, Manuel González, Mostafa Mbekhta (2000)

Studia Mathematica

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We prove that if some power of an operator is ergodic, then the operator itself is ergodic. The converse is not true.

Local ergodic theorems.

Teresa Bermúdez, Manuel González, Mostafa Mbekhta (1998)

Extracta Mathematicae

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On new spectral multiplicities for ergodic maps

Alexandre I. Danilenko (2010)

Studia Mathematica

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It is shown that each subset of positive integers that contains 2 is realizable as the set of essential values of the multiplicity function for the Koopman operator of some weakly mixing transformation.

Hopf's ratio ergodic theorem by inducing

Roland Zweimüller (2004)

Colloquium Mathematicae

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We present a very quick and easy proof of the classical Stepanov-Hopf ratio ergodic theorem, deriving it from Birkhoff's ergodic theorem by a simple inducing argument.

Uniformly ergodic A-contractions on Hilbert spaces

Laurian Suciu (2009)

Studia Mathematica

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We study the concept of uniform (quasi-) A-ergodicity for A-contractions on a Hilbert space, where A is a positive operator. More precisely, we investigate the role of closedness of certain ranges in the uniformly ergodic behavior of A-contractions. We use some known results of M. Lin, M. Mbekhta and J. Zemánek, and S. Grabiner and J. Zemánek, concerning the uniform convergence of the Cesàro means of an operator, to obtain similar versions for A-contractions. Thus, we continue the study...