Geodesic
Estimates of the Least Positive Root of the Sum of a Sine Series with Monotone Coefficients
Matematičeskie zametki, Tome 96 (2014) no. 5, pp. 747-761 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper, the extremal problem of finding the infimum of the positive roots of the sum of a sine series with monotone coefficients for special subclasses of such series is solved.
Keywords: sine series, trigonometric polynomial, roots of the sum of a series.
Mots-clés : Abel transformation 
@article{MZM_2014_96_5_a10,
     author = {A. Yu. Popov},
     title = {Estimates of the {Least} {Positive} {Root} of the {Sum} of a {Sine} {Series} with {Monotone} {Coefficients}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {747--761},
     year = {2014},
     volume = {96},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_5_a10/}
}
TY  - JOUR
AU  - A. Yu. Popov
TI  - Estimates of the Least Positive Root of the Sum of a Sine Series with Monotone Coefficients
JO  - Matematičeskie zametki
PY  - 2014
SP  - 747
EP  - 761
VL  - 96
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_2014_96_5_a10/
LA  - ru
ID  - MZM_2014_96_5_a10
ER  - 
%0 Journal Article
%A A. Yu. Popov
%T Estimates of the Least Positive Root of the Sum of a Sine Series with Monotone Coefficients
%J Matematičeskie zametki
%D 2014
%P 747-761
%V 96
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_2014_96_5_a10/
%G ru
%F MZM_2014_96_5_a10
A. Yu. Popov. Estimates of the Least Positive Root of the Sum of a Sine Series with Monotone Coefficients. Matematičeskie zametki, Tome 96 (2014) no. 5, pp. 747-761. http://geodesic.mathdoc.fr/item/MZM_2014_96_5_a10/

[1] P. Hartman, A. Wintner, “On sine series with monotone coefficients”, J. London Math. Soc., 28 (1953), 102–104 | DOI | MR | Zbl

[2] P. Hartman, A. Wintner, “On the behavior of Fourier sine transforms near the origin”, Proc. Amer. Math. Soc., 2 (1951), 398–400 | DOI | MR | Zbl

[3] R. P. Boas Jr., Integrability Theorems for Trigonometric Transforms, Ergeb. Math. Grenzgeb., 38, Springer-Verlag, Berlin, 1967 | MR | Zbl

[4] L. Vietoris, “Über das Vorzeichen gewisser trigonometricher Summen”, Österr. Acad. Wiss. Math.-Natur. Kl. S.-B. Abt. II, 167 (1958), 125–135 | Zbl

[5] A. S. Belov, “O primerakh trigonometricheskikh ryadov s neotritsatelnymi chastnymi summami”, Matem. sb., 186:4 (1995), 21–46 | MR | Zbl