Spectral criteria for existence of generalized ergodic transforms
Teoriâ veroâtnostej i ee primeneniâ, Tome 41 (1996) no. 2, pp. 251-271
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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.
@article{TVP_1996_41_2_a1,
author = {V. F. Gaposhkin},
title = {Spectral criteria for~existence of~generalized ergodic transforms},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {251--271},
year = {1996},
volume = {41},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1996_41_2_a1/}
}
V. F. Gaposhkin. Spectral criteria for existence of generalized ergodic transforms. Teoriâ veroâtnostej i ee primeneniâ, Tome 41 (1996) no. 2, pp. 251-271. http://geodesic.mathdoc.fr/item/TVP_1996_41_2_a1/