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This article is cited in 19 scientific papers (total 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
Citation:
V. F. Gaposhkin, “Spectral criteria for existence of generalized ergodic transforms”, Teor. Veroyatnost. i Primenen., 41:2 (1996), 251–271; Theory Probab. Appl., 41:2 (1997), 247–264
Linking options:
https://www.mathnet.ru/eng/tvp2931https://doi.org/10.4213/tvp2931 https://www.mathnet.ru/eng/tvp/v41/i2/p251
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Abstract page: | 232 | Full-text PDF : | 157 | First page: | 6 |
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