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.
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页码：959 / 971
页数：13
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