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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Sampling theorems for nonstationary random processes

Author: Alan J. Lee
Journal: Trans. Amer. Math. Soc. 242 (1978), 225-241
MSC: Primary 60G99; Secondary 42A68, 94A05
MathSciNet review: 0482995
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Abstract: Consider a second order stochastic process $ \{ X(t),t \in \textbf{R}\} $, and let $ H(X)$ be the Hilbert space generated by the random variables of the process. The process is said to be linearly determined by its samples $ \{ X(nh),n \in \textbf{Z}\} $ if the random variables $ X(nh)$ generate $ H(X)$. In this paper we give a sufficient condition for a wide class of nonstationary processes to be determined by their samples, and present sampling theorems for such processes. We also consider similar problems for harmonizable processes indexed by LCA groups having suitable subgroups.

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PII: S 0002-9947(1978)0482995-6
Keywords: Sampling theorem, reproducing kernel Hilbert space, Sobolev space, Fourier series, periodic distribution, harmonizable process
Article copyright: © Copyright 1978 American Mathematical Society