Geodesic
The Measure of the Set of Zeros of the Sum of a Nondegenerate Sine Series with Monotone Coefficients in the Closed Interval $[0,\pi]$
Matematičeskie zametki, Tome 103 (2018) no. 4, pp. 576-581.

Voir la notice de l'article provenant de la source Math-Net.Ru

Nonzero sine series with monotone coefficients tending to zero are considered. It is shown that the measure of the set of those zeros of such a series which belong to $[0,\pi]$ cannot exceed $\pi/3$. Moreover, if this value is attained, then almost all zeros belong to the closed interval $[2\pi/3,\pi]$.
Keywords: sine series, zeros of a function, measure of a set.
Mots-clés : monotone coefficients 
@article{MZM_2018_103_4_a8,
     author = {K. A. Oganesyan},
     title = {The {Measure} of the {Set} of {Zeros} of the {Sum} of a {Nondegenerate} {Sine} {Series} with {Monotone} {Coefficients} in the {Closed} {Interval} $[0,\pi]$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {576--581},
     publisher = {mathdoc},
     volume = {103},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a8/}
}
TY  - JOUR
AU  - K. A. Oganesyan
TI  - The Measure of the Set of Zeros of the Sum of a Nondegenerate Sine Series with Monotone Coefficients in the Closed Interval $[0,\pi]$
JO  - Matematičeskie zametki
PY  - 2018
SP  - 576
EP  - 581
VL  - 103
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a8/
LA  - ru
ID  - MZM_2018_103_4_a8
ER  - 
%0 Journal Article
%A K. A. Oganesyan
%T The Measure of the Set of Zeros of the Sum of a Nondegenerate Sine Series with Monotone Coefficients in the Closed Interval $[0,\pi]$
%J Matematičeskie zametki
%D 2018
%P 576-581
%V 103
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a8/
%G ru
%F MZM_2018_103_4_a8
K. A. Oganesyan. The Measure of the Set of Zeros of the Sum of a Nondegenerate Sine Series with Monotone Coefficients in the Closed Interval $[0,\pi]$. Matematičeskie zametki, Tome 103 (2018) no. 4, pp. 576-581. http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a8/

[1] V. F. Gaposhkin, “O nulyakh trigonometricheskikh ryadov s monotonnymi koeffitsientami”, Izv. vuzov. Matem., 1981, no. 9, 13–15 | MR | Zbl

[2] M. I. Dyachenko, “O ryadakh Fure s monotonno ubyvayuschimi koeffitsientami i nekotorykh voprosakh gladkosti sopryazhennykh funktsii”, Soobsch. AN Gruz. SSR, 104:3 (1981), 533–536 | MR | Zbl

[3] A. S. Belov, “Stepennye ryady i krivye Peano”, Izv. AN SSSR. Ser. matem., 49:4 (1985), 675–704 | MR | Zbl

[4] M. I. Dyachenko, “Teoriya funktsii i priblizhenii”, Trudy 2-i Saratovskoi zimnei shkoly, Ch. 2 (24 yanvarya – 5 fevralya 1984 goda), Izd-vo Saratovskogo un-ta, 1986, 101–104

[5] M. I. D'yachenko, “On some properties of trigonometric series with monotone decreasing coefficients”, Anal. Math., 10:3 (1984), 193–205 | DOI | MR | Zbl