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

被引：3

作者：

Zastavnyi, V. P. ^{[1
]}

机构：

[1] Donetsk Natl Univ, UA-83114 Donetsk, Ukraine

来源：

MATHEMATICAL NOTES | 2020年 / 107卷 / 5-6期

关键词：

positive definite functions; Fourier transform; Bochner-Khinchine theorem; piece-wise linear functions with equidistant nodes;

D O I：

10.1134/S0001434620050272

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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

引用

页码：959 / 971

页数：13

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