Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Iofina T. V. Approximation of Functions by Borel Means of Fourier Series with Respect to Multiplicative Systems. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2011, vol. 11, iss. 3, pp. 15-21. DOI: 10.18500/1816-9791-2011-11-3-1-15-21

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
15.07.2011
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Language: 
Russian
Heading: 
Mathematics
UDC: 
517.51
DOI: 
10.18500/1816-9791-2011-11-3-1-15-21

Approximation of Functions by Borel Means of Fourier Series with Respect to Multiplicative Systems

Autors: 
Iofina T. V., Saratov State University
Abstract: 

In the present paper we consider Borel means of Fourier series with respect to Vilenkin systems with bounded generating sequence and obtain some estimates of approximation by this means in L p , uniform and Holder type norm in classes of functions with given majorant of best approximation or modulus of continuity. In the trigonometric case similar results were established by P.Chandra, L.Rempulska and K.Tomczak.

Key words: 
Vilenkin systems with bounded generating sequence
Borel means
Holder type metric
Lp-norm
uniform norm
References: 
  1. Харди Г. Расходящиеся ряды. М.: Изд-во иностр. лит., 1951. 504 с.
  2. Prossdorf S.  ̈ Zur Konvergenz der Fourierreihen holderstetiger Funktionen // Math. Nachr. 1975. Vol. 69.  ̈ P. 7–14.
  3. Chandra P. Degree of approximation of functions in the Holder metric by Borel means // J. Math. Anal. Appl.  ̈ 1990. Vol. 149. P. 236–248.
  4. Das G., Ojha A. K., Ray B. K. Degree of approximation of functions associated with Hardy – Littlewood series in the Holder metric by Borel means // J. Math. Anal. Appl.  ̈ 1998. Vol. 210, No 2. P. 279–293.
  5. Rempulska L., Tomczak K. On Euler and Borel means of Fourier series in Holder spases // Proc. of A. Razmadze  ̈ Math. Institute. 2006. Vol. 140. P. 141–153.
  6. Iofina T. V., Volosivets S. S. On the degree on approximation by means of Fourier – Vilenkin series in Holder and L p norm // East J. on Approximations. 2009. Vol. 15, No 2. P. 143–158.
  7. Голубов Б. И., Ефимов А. В., Скворцов В. А. Ряды и преобразования Уолша. Теория и применения. M.: Наука, 1987. 344 с.
  8. Schipp F. On L p -norm convergence of series with respect to product systems // Anal. Math. 1976. Vol. 2. P. 49–64.
  9. Simon P. Verallgemeinerte Walsch – Fourierreihen // Acta Math. Hungar. 1976. Vol. 27, No 3–4. P. 329–341.
  10. 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.
  11. Ахиезер Н. И. Лекции по теории аппроксимаций. М.: ГИТТЛ, 1947. 324 с.
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