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

共 50 条

[31] Estimates with Sharp Constants of the Sums of Sine Series with Monotone Coefficients of Certain Classes in Terms of the Salem Majorant
Popov, A. Yu.
Solodov, A. P.
[J]. MATHEMATICAL NOTES, 2018, 104 (5-6) : 702 - 711
[32] Estimates with Sharp Constants of the Sums of Sine Series with Monotone Coefficients of Certain Classes in Terms of the Salem Majorant
A. Yu. Popov
A. P. Solodov
[J]. Mathematical Notes, 2018, 104 : 702 - 711
[33] Exact Lower Estimate of the Upper Limit of the Ratio of the Sum of Sine Series with Monotone Coefficients to its Majorant
Popov, A. Yu.
Solodov, A. P.
[J]. MOSCOW UNIVERSITY MATHEMATICS BULLETIN, 2014, 69 (04) : 169 - 173
[34] The Calculation of the Error of a Sine Series Approximation with Coefficients from the Class of General Monotone Sequences Order r
Imron, Moch. Aruman
[J]. 8TH ANNUAL BASIC SCIENCE INTERNATIONAL CONFERENCE: COVERAGE OF BASIC SCIENCES TOWARD THE WORLD'S SUSTAINABILITY CHALLANGES, 2018, 2021
[35] Exact lower estimate of the upper limit of the ratio of the sum of sine series with monotone coefficients to its majorant
Popov A.Y.
Solodov A.P.
[J]. Moscow University Mathematics Bulletin, 2014, 69 (4) : 169 - 173
[36] Series with monotone coefficients by Walsh system
K. A. Navasardyan
[J]. Journal of Contemporary Mathematical Analysis, 2007, 42 (5) : 258 - 269
[37] Trigonometric series with general monotone coefficients
Tikhonov, S.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 326 (01) : 721 - 735
[38] ZEROS OF TRIGONOMETRICAL SERIES WITH MONOTONE COEFFICIENTS
GAPOSHKIN, VF
[J]. IZVESTIYA VYSSHIKH UCHEBNYKH ZAVEDENII MATEMATIKA, 1981, (09): : 13 - 15
[39] Series by Haar system with monotone coefficients
M. G. Grigoryan
[J]. Journal of Contemporary Mathematical Analysis, 2007, 42 (4) : 205 - 218
[40] ZEROS OF TRIGONOMETRIC SERIES WITH MONOTONE COEFFICIENTS
BELOV, AS
[J]. IZVESTIYA VYSSHIKH UCHEBNYKH ZAVEDENII MATEMATIKA, 1989, (12): : 3 - 8

← 1 2 3 4 5 →