Geodesic
A Generalization of Schep's Theorem
Matematičeskie zametki, Tome 107 (2020) no. 6, pp. 873-887

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Schep proved that, for a piecewise linear function with nodes at integer points, positive definiteness on $\mathbb{R}$ is equivalent to positive definiteness on $\mathbb{Z}$. In this paper, a similar theorem for an entire function of exponential type is proved, and a generalization Schep's theorem is obtained.
Keywords: positive definite functions, Bochner–Khinchine theorem, piecewise linear functions with equidistant nodes.
Mots-clés : Fourier transform 
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     author = {V. P. Zastavnyi},
     title = {A {Generalization} of {Schep's} {Theorem}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {873--887},
     publisher = {mathdoc},
     volume = {107},
     number = {6},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_107_6_a6/}
}
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V. P. Zastavnyi. A Generalization of Schep's Theorem. Matematičeskie zametki, Tome 107 (2020) no. 6, pp. 873-887. http://geodesic.mathdoc.fr/item/MZM_2020_107_6_a6/