Chatterji, S. D. Positive definite kernels. (English) Zbl 0584.60050 Bol. Soc. Mat. Mex., II. Ser. 28, 59-65 (1983). 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 Cited in 2 Documents MSC: 60G25 Prediction theory (aspects of stochastic processes) 47A20 Dilations, extensions, compressions of linear operators 46A99 Topological linear spaces and related structures Keywords:factorization theorem; positive-definite operator valued kernels Citations:Zbl 0516.47009; Zbl 0473.46003 PDFBibTeX XMLCite \textit{S. D. Chatterji}, Bol. Soc. Mat. Mex., II. Ser. 28, 59--65 (1983; Zbl 0584.60050)