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Positive definite kernels on the set of integers, stability, some properties and applications. (English) Zbl 07858109

Summary: We define and investigate a class of positive definite kernel, a so-called equivalent-kernel. We formulate and prove an analogous of Paley-Wiener theorem in the context of positive definite kernel. The main ingredient in the proof is the Kolmogorov decomposition. Finally, some applications to stochastic processes are given.

MSC:

42A82 Positive definite functions in one variable harmonic analysis
60G10 Stationary stochastic processes
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