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...
| Main Authors: | , , |
|---|---|
| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
AIP Publishing
2018
|
| Subjects: | |
| Online Access: | 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 |
| _version_ | 1848821692799909888 |
|---|---|
| author | Ahmedov, Anvarjon A. Matarneh, Ehab Hishamuddin, Zainuddin |
| author_facet | Ahmedov, Anvarjon A. Matarneh, Ehab Hishamuddin, Zainuddin |
| author_sort | Ahmedov, Anvarjon A. |
| building | UMP Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-15T02:29:23Z |
| format | Conference or Workshop Item |
| id | ump-22957 |
| institution | Universiti Malaysia Pahang |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T02:29:23Z |
| publishDate | 2018 |
| publisher | AIP Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 (Published) https://doi.org/10.1063/1.5041534 |
| 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 |
| title | 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_short | 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 |
| topic | QA Mathematics QC Physics |
| 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 |