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