THE SETS OF POSITIVITY OF SINE SERIES WITH MONOTONE COEFFICIENTS

被引：0

作者：

Oganesyan, K. ^{[1
,2
]}

机构：

[1] Univ Autonoma Barcelona, Ctr Recerca Matemat, Barcelona, Spain

[2] Lomonosov Moscow State Univ, Moscow Ctr Fundamental & Appl Math, Leninskie Gory 1, Moscow 119991, Russia

来源：

ACTA MATHEMATICA HUNGARICA | 2020年 / 162卷 / 02期

关键词：

sine series; monotone coefficients; measure of a set; set of positivity; ZEROS;

D O I：

10.1007/s10474-020-01089-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the sums of nondegenerate sine series with monotone coefficients and consider the sets of positivity of such functions. We obtain the sharp lower estimate of the measure of such a set on [pi/2, pi] and a new lower bound on its measure on [0, pi]. It is shown that the latter measure is at least pi/2+ 0.24 and in the case of fulfilling special conditions it is at least 2 pi d/3, which is an unimprovable estimate.

引用

页码：705 / 721

页数：17

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