On the divergence of spectral expansions of elliptic differential operators - Ahmedov, Anvarjon (Universiti Putra Malaysia Press, 2011)
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.