On the divergence of spectral expansions of elliptic differential operators
In this paper we consider spectral expansions of functions from Nikol'skii classes Hap (Rn), related to selfadjoint extensions of elliptic differential operators A(D) of order m in Rn. We construct a continuous function from Nikol'skii class with pa < N, such that the Riesz means of spe...
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| Format: | Article |
| Language: | English |
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Universiti Putra Malaysia Press
2011
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| Online Access: | http://psasir.upm.edu.my/id/eprint/23261/ http://psasir.upm.edu.my/id/eprint/23261/1/23261.pdf |
| _version_ | 1848844707981950976 |
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| author | Ahmedov, Anvarjon Ashurov, Ravshan |
| author_facet | Ahmedov, Anvarjon Ashurov, Ravshan |
| author_sort | Ahmedov, Anvarjon |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper we consider spectral expansions of functions from Nikol'skii classes Hap (Rn), related to selfadjoint extensions of elliptic differential operators A(D) of order m in Rn. We construct a continuous function from Nikol'skii class with pa < N, such that the Riesz means of spectral expansion of which diverge at the origin. This result demonstrates sharpness of the condition pa > N obtained earlier by Alimov (1976) for uniform convergence of spectral expansions, related to elliptic differential operators. |
| first_indexed | 2025-11-15T08:35:12Z |
| format | Article |
| id | upm-23261 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T08:35:12Z |
| publishDate | 2011 |
| publisher | Universiti Putra Malaysia Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-232612015-05-27T07:55:18Z http://psasir.upm.edu.my/id/eprint/23261/ On the divergence of spectral expansions of elliptic differential operators Ahmedov, Anvarjon Ashurov, Ravshan In this paper we consider spectral expansions of functions from Nikol'skii classes Hap (Rn), related to selfadjoint extensions of elliptic differential operators A(D) of order m in Rn. We construct a continuous function from Nikol'skii class with pa < N, such that the Riesz means of spectral expansion of which diverge at the origin. This result demonstrates sharpness of the condition pa > N obtained earlier by Alimov (1976) for uniform convergence of spectral expansions, related to elliptic differential operators. Universiti Putra Malaysia Press 2011 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/23261/1/23261.pdf Ahmedov, Anvarjon and Ashurov, Ravshan (2011) On the divergence of spectral expansions of elliptic differential operators. Malaysian Journal of Mathematical Sciences, 5 (2). pp. 185-196. ISSN 1823-8343 http://einspem.upm.edu.my/journal/fullpaper/vol5no2/3.%20anvarjon%20et%20al.pdf |
| spellingShingle | Ahmedov, Anvarjon Ashurov, Ravshan On the divergence of spectral expansions of elliptic differential operators |
| title | On the divergence of spectral expansions of elliptic differential operators |
| title_full | On the divergence of spectral expansions of elliptic differential operators |
| title_fullStr | On the divergence of spectral expansions of elliptic differential operators |
| title_full_unstemmed | On the divergence of spectral expansions of elliptic differential operators |
| title_short | On the divergence of spectral expansions of elliptic differential operators |
| title_sort | on the divergence of spectral expansions of elliptic differential operators |
| url | http://psasir.upm.edu.my/id/eprint/23261/ http://psasir.upm.edu.my/id/eprint/23261/ http://psasir.upm.edu.my/id/eprint/23261/1/23261.pdf |