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On the divergence of spectral expansions of elliptic differential operators


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
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