The almost everywhere convergence of the eigenfunction expansions from Liouville classes corresponding to the elliptic operators

Many problems of mathematical physics can be solved by separation methods of partial differential equations. By application of separation method, a solution of the partial differential equation can be represented in terms of eigenfunction expansions of elliptic differential operator. To obtain the s...

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Main Authors:	Ahmedov, Anvarjon A., Matarneh, Ehab, Hishamuddin, Zainuddin
Format:	Conference or Workshop Item
Language:	English
Published:	AIP Publishing 2018
Subjects:	QA Mathematics QC Physics
Online Access:	http://umpir.ump.edu.my/id/eprint/22957/ http://umpir.ump.edu.my/id/eprint/22957/ http://umpir.ump.edu.my/id/eprint/22957/1/The%20almost%20everywhere%20convergence%20of%20the%20eigenfunction%20expansions%20from%20Liouville%20classes%20.pdf

id	ump-22957
recordtype	eprints
spelling	ump-229572019-06-11T06:49:40Z http://umpir.ump.edu.my/id/eprint/22957/ The almost everywhere convergence of the eigenfunction expansions from Liouville classes corresponding to the elliptic operators Ahmedov, Anvarjon A. Matarneh, Ehab Hishamuddin, Zainuddin QA Mathematics QC Physics Many problems of mathematical physics can be solved by separation methods of partial differential equations. By application of separation method, a solution of the partial differential equation can be represented in terms of eigenfunction expansions of elliptic differential operator. To obtain the solution from its eigenfunction expansion one has to investigate the conditions for convergence of such expansions. In this paper, the problems of almost everywhere convergence of the eigenfunction expansions of the functions from Liouville classes are investigated. The Lebesgue constant corresponding to the elliptic polynomials are estimated. The Jackson Theorem is applied to prove the convergence of multiple Fourier series in the classes of Liouville. AIP Publishing 2018-06 Conference or Workshop Item PeerReviewed pdf en http://umpir.ump.edu.my/id/eprint/22957/1/The%20almost%20everywhere%20convergence%20of%20the%20eigenfunction%20expansions%20from%20Liouville%20classes%20.pdf Ahmedov, Anvarjon A. and Matarneh, Ehab and Hishamuddin, Zainuddin (2018) The almost everywhere convergence of the eigenfunction expansions from Liouville classes corresponding to the elliptic operators. In: 25th National Symposium on Mathematical Sciences: Mathematical Sciences as the Core of Intellectual Excellence (SKSM 2017), 27-29 August 2017 , Kuantan, Pahang. , 1974. ISSN 0094-243X https://doi.org/10.1063/1.5041534
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Malaysia Pahang
building	UMP Institutional Repository
collection	Online Access
language	English
topic	QA Mathematics QC Physics
spellingShingle	QA Mathematics QC Physics Ahmedov, Anvarjon A. Matarneh, Ehab Hishamuddin, Zainuddin The almost everywhere convergence of the eigenfunction expansions from Liouville classes corresponding to the elliptic operators
description	Many problems of mathematical physics can be solved by separation methods of partial differential equations. By application of separation method, a solution of the partial differential equation can be represented in terms of eigenfunction expansions of elliptic differential operator. To obtain the solution from its eigenfunction expansion one has to investigate the conditions for convergence of such expansions. In this paper, the problems of almost everywhere convergence of the eigenfunction expansions of the functions from Liouville classes are investigated. The Lebesgue constant corresponding to the elliptic polynomials are estimated. The Jackson Theorem is applied to prove the convergence of multiple Fourier series in the classes of Liouville.
format	Conference or Workshop Item
author	Ahmedov, Anvarjon A. Matarneh, Ehab Hishamuddin, Zainuddin
author_facet	Ahmedov, Anvarjon A. Matarneh, Ehab Hishamuddin, Zainuddin
author_sort	Ahmedov, Anvarjon A.
title	The almost everywhere convergence of the eigenfunction expansions from Liouville classes corresponding to the elliptic operators
title_short	The almost everywhere convergence of the eigenfunction expansions from Liouville classes corresponding to the elliptic operators
title_full	The almost everywhere convergence of the eigenfunction expansions from Liouville classes corresponding to the elliptic operators
title_fullStr	The almost everywhere convergence of the eigenfunction expansions from Liouville classes corresponding to the elliptic operators
title_full_unstemmed	The almost everywhere convergence of the eigenfunction expansions from Liouville classes corresponding to the elliptic operators
title_sort	almost everywhere convergence of the eigenfunction expansions from liouville classes corresponding to the elliptic operators
publisher	AIP Publishing
publishDate	2018
url	http://umpir.ump.edu.my/id/eprint/22957/ http://umpir.ump.edu.my/id/eprint/22957/ http://umpir.ump.edu.my/id/eprint/22957/1/The%20almost%20everywhere%20convergence%20of%20the%20eigenfunction%20expansions%20from%20Liouville%20classes%20.pdf
first_indexed	2023-09-18T22:34:11Z
last_indexed	2023-09-18T22:34:11Z
_version_	1777416484995203072

The almost everywhere convergence of the eigenfunction expansions from Liouville classes corresponding to the elliptic operators

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