Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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


For citation:

Burmistrova M. D. On Laguerre Expansions Summability by the Linear Methods. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2008, vol. 8, iss. 1, pp. 15-20. DOI: 10.18500/1816-9791-2008-8-1-15-20

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
03.03.2008
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Russian
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UDC: 
517.5

On Laguerre Expansions Summability by the Linear Methods

Autors: 
Burmistrova M. D., OOO «Zirvan»
Abstract: 

This paper studies a problem of Laguerre expansions summability via methods defined by triangular matrices. The conditions on a matrix and an expandable function are obtained to guarantee the convergence of corresponding linear means at the Lebesgue point t = 0.

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References: 
  1. Сегё Г. Ортогональные многочлены. М.: Физматгиз, 1962.
  2. Фаддеев Д.К. О представлении суммируемых функций сингулярными интегралами в точках Lebesgue’а // Матем. cб. 1936. T. 1/43, No 3. C. 351–368.
  3. Зигмунд А. Тригонометрические ряды. М.: Мир, 1965. Т. I.
  4. Колмогоров А.Н., Фомин С.В. Элементы теории функций и функционального анализа. М.: Наука, 1981.
  5. Askey R., Wainger S. Mean convergence of expansions in Laguerre and Hermite series // Amer. J. Math. 1965.
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