For citation:
Fadeev R. N. Uniform Convergence of the Series with Respect to Multiplicative Systems. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 1, pp. 36-40. DOI: 10.18500/1816-9791-2013-13-1-1-36-40, EDN: SMXXHV
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online:
15.02.2013
Full text:
(downloads: 201)
Language:
Russian
Heading:
UDC:
517.518
EDN:
SMXXHV
Uniform Convergence of the Series with Respect to Multiplicative Systems
Autors:
Fadeev Roman Nikolaevich, Saratov State University
Abstract:
Two theorems on uniform convergence and boundedness of partial sums for the series with generalized monotone coefficients with respect to multiplicative systems are proved.
Key words:
References:
- Голубов Б. И. Ефимов А. В. Скворцов В. А. Ряды и преобразования Уолша. М. : Наука, 1987. 344 c. [Golubov B., Efimov A., Skvortsov V. Walsh series and transforms. Dordrecht; Boston; London : Kluver Academic Publishers, 1991.]
- Тихонов С. Ю. О равномерной сходимости тригонометрического ряда // Мат. заметки. 2007. Т. 81, № 2. С. 304–310. [Tikhonov S. Yu. On the uniform convergence of trigonometric series // Math. Notes. 2007. Vol. 81, № 2. P. 268–274.]
- Leindler L. On the uniform convergence and boundedness of a certain class of sine series // Analysis Math. 2001. Vol. 1, № 4. P. 279–285.
- Агаев Г. Н., Виленкин Н. Я., Джафарли Г. М., Рубинштейн А. И. Мультипликативные системы функций и гармонический анализ на нуль-мерных группах. Баку : Элм, 1981. 180 с. [Agaev G. N., Vilenkin N. Ya., Dzafarli G. M., Rubinstein A. I. Multiplicative Systems of Functions and Harmonic Analysis on Zero-Dimensional Groups. Baku : Elm Publisher, 1981. 180 p.]
- Бари Н. К. Тригонометрические ряды. М. : Физматгиз, 1961. 936 с. [Bari N. K. Trigonometric Series. Moscow : Fizmatgiz, 1961. 936 p.]
Received:
19.08.2012
Accepted:
10.01.2013
Published:
15.02.2013
- 1010 reads