Celebratio Mathematica — Rosenblatt

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Works connected to William C. Hoffman

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M. Rosenblatt: “The multidimensional prediction problem,” pp. 99–111 in Statistical methods of radio wave propagation (Los Angeles, 18–20 June 1958). Edited by W. C. Hoffman. Pergamon Press (New York), 1960. A closely related paper was published in Proc. Natl. Acad. Sci. U.S.A. 43:11 (1957). incollection

G. Szegő discussed a minimum problem and an allied problem on the representation of a non-negative function as the absolute square of a one-sided trigonometric series in two fundamental papers [1920, 1921]. In later years it was realized that Szegő’s problem is the complete analytic couterpart of a one-dimensional statistical prediction problem (see [Doob 1953, Chapter 12], for a full discussion of the problem and references to the literature). Very recently considerable interest has arisen in matrix analogues of Szegő’s results, especially, since they are the analytic counterparts of corresponding multidimensional prediction problems. In [Helson and Lowdenslager 1957; Wiener and Masani 1957] results in this direction have been obtained. This survey paper derives similar results (with similar techniques) by reducing aspects of the multidimensional problem to the corresponding one-dimensional problem.