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Transactions of the American Mathematical Society

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On the alternating projections theorem and bivariate stationary stochastic processes


Author: Habib Salehi
Journal: Trans. Amer. Math. Soc. 128 (1967), 121-134
MSC: Primary 60.50; Secondary 47.00
DOI: https://doi.org/10.1090/S0002-9947-1967-0214135-5
MathSciNet review: 0214135
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Abstract: In this paper we shall first use the theorem of von Neumann on alternating projections to obtain an algorithm for finding the projection of an element x in a Hilbert space $\mathcal {H}$ onto the subspace spanned by $\mathcal {H}$-valued orthogonally scattered measures ${\xi _1}$ and ${\xi _2}$. We then specialize this algorithm to the case that ${\xi _1}$ and ${\xi _2}$ are the canonical measures of the components of a bivariate stationary stochastic process (SP), and thereby get an algorithm for finding the best linear predictor in the time domain.


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Article copyright: © Copyright 1967 American Mathematical Society