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Positive definite kernels. (English) Zbl 0584.60050

The author presents a very general factorization theorem valid for positive-definite operator valued kernels. However the proofs from another author’s paper, Prediction theory and harmonic analysis, Pesi Masani Vol. 331, 23-36 (1983; Zbl 0516.47009), where a special case was studied need no changes whatsoever. Cf. also a related paper by J. Gorniak and the reviewer, Stud. Math. 69, 235-246 (1981; Zbl 0473.46003).

The factorization theorem is preceded by an introductory survey of the uses of scalar valued positive definite kernels which is of independent interest.

Reviewer: A.Weron
MSC:
60G25Prediction theory
47A20Dilations, extensions and compressions of linear operators
46A99Topological linear spaces