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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

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Official URL: http://einspem.upm.edu.my/journal/fullpaper/vol5no...

Abstract

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.

Item Type:Article
Keyword:Fourier integral; Spectral expansions of the differential operators; Spectral function; Riesz means
Faculty or Institute:Faculty of Engineering
Institute for Mathematical Research
Institute of Advanced Technology
Publisher:Universiti Putra Malaysia Press
ID Code:23261
Deposited By: Muizzudin Kaspol
Deposited On:03 Nov 2014 15:43
Last Modified:27 May 2015 15:55

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