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 | References | Similar Articles | Additional Information

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