Wiener's problem for positive definite functions

被引：5

作者：

Gorbachev, D. V. ^{[1
]}

Tikhonov, S. Yu. ^{[2
,3
,4
]}

机构：

[1] Tula State Univ, Dept Appl Math & Comp Sci, Tula 300012, Russia

[2] Ctr Recerca Matemat, Campus Bellaterra,Edifici C, Barcelona 08193, Spain

[3] ICREA, Pg Lluis Co 23, Barcelona 08010, Spain

[4] Univ Autonoma Barcelona, E-08193 Barcelona, Spain

来源：

MATHEMATISCHE ZEITSCHRIFT | 2018年 / 289卷 / 3-4期

关键词：

Positive definite function; Wiener's problem; Hlawka's inequality; Sharp constant; Linear programming bound problem; SPHERE PACKING PROBLEM; PERIODIC-FUNCTIONS; EXTREMAL PROBLEM; TURAN; FAILURE; SERIES; BOUNDS;

D O I：

10.1007/s00209-017-1978-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the sharp constant in Wiener's inequality for positive definite functions Tn | f | 2 dx = Wn( D)| D|- 1 D | f | 2 dx, D. Tn Wiener proved that , . Hlawka showed that , where D is an origin-symmetric convex body. We sharpen Hlawka's estimates for D being the ball and the cube . In particular, we prove that . We also obtain a lower bound of . Moreover, for a cube with we obtain that . Our proofs are based on the interrelation between Wiener's problem and the problems of Turan and Delsarte.

引用

页码：859 / 874

页数：16

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