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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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Main Authors: Ahmedov, Anvarjon, Ashurov, Ravshan
Format: Article
Language:English
Published: Universiti Putra Malaysia Press 2011
Online Access:http://psasir.upm.edu.my/id/eprint/23261/1/23261.pdf
http://psasir.upm.edu.my/id/eprint/23261/
http://einspem.upm.edu.my/journal/fullpaper/vol5no2/3.%20anvarjon%20et%20al.pdf
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spelling my.upm.eprints.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
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
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.
format Article
author Ahmedov, Anvarjon
Ashurov, Ravshan
spellingShingle Ahmedov, Anvarjon
Ashurov, Ravshan
On the divergence of spectral expansions of elliptic differential operators
author_facet Ahmedov, Anvarjon
Ashurov, Ravshan
author_sort Ahmedov, Anvarjon
title On the divergence of spectral expansions of elliptic differential operators
title_short 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_sort on the divergence of spectral expansions of elliptic differential operators
publisher Universiti Putra Malaysia Press
publishDate 2011
url http://psasir.upm.edu.my/id/eprint/23261/1/23261.pdf
http://psasir.upm.edu.my/id/eprint/23261/
http://einspem.upm.edu.my/journal/fullpaper/vol5no2/3.%20anvarjon%20et%20al.pdf
_version_ 1643828005223530496
score 13.251813

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