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On the divergence of spectral expansions of elliptic differential operators


Citation

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

Abstract / Synopsis

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.


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Additional Metadata

Item Type: Article
Divisions: Faculty of Engineering
Institute for Mathematical Research
Institute of Advanced Technology
Publisher: Universiti Putra Malaysia Press
Keywords: Fourier integral; Spectral expansions of the differential operators; Spectral function; Riesz means
Depositing User: Muizzudin Kaspol
Date Deposited: 03 Nov 2014 07:43
Last Modified: 27 May 2015 07:55
URI: http://psasir.upm.edu.my/id/eprint/23261
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