This article is cited in 19 papers

Spectral criteria for existence of generalized ergodic transforms

V. F. Gaposhkin

Moscow State University of Railway Communications

Abstract: Conditions are studied for a.e. convergence of one-sided and two-sided ergodic transforms
$$ \sum_1^\infty b_kT^kf(x) \text{ and } \sum_{-\infty}^\infty b_kT^kf(x), $$
where $T$ is a unitary operator in $L^2$. Criteria for existence of these transforms are obtained in terms of the properties of the operator spectral measure. Similar results are stated for normal operators and for stationary and harmonizable stochastic processes

Keywords: unitary operators, normal operators, stationary processes, harmonizable processes, spectral measure, ergodic transforms, convergence almost everywhere.

Received: 16.06.1993

DOI: 10.4213/tvp2931

 English version: Theory of Probability and its Applications, 1997, 41:2, 247–264

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