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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On the alternating projections theorem and bivariate stationary stochastic processes
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by Habib Salehi PDF
Trans. Amer. Math. Soc. 128 (1967), 121-134 Request permission

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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Additional Information
  • © Copyright 1967 American Mathematical Society
  • 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