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A Generalization of Schep’s Theorem on the Positive Definiteness of a Piecewise Linear Function

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Abstract

Schep proved that, for a piecewise linear function with nodes at integer points, positive definiteness on ℝ is equivalent to positive definiteness on ℤ. In this paper, a similar theorem for an entire function of exponential type is proved, and a generalization Schep’s theorem is obtained.

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  1. Donetsk National University, Donetsk, 83114, Ukraine

    V. P. Zastavnyi

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  1. V. P. Zastavnyi
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Correspondence to V. P. Zastavnyi.

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Russian Text © The Author(s), 2020, published in Matematicheskie Zametki, 2020, Vol. 107, No. 6, pp. 873–887.

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Zastavnyi, V.P. A Generalization of Schep’s Theorem on the Positive Definiteness of a Piecewise Linear Function. Math Notes 107, 959–971 (2020). https://doi.org/10.1134/S0001434620050272

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