On the Smoothness of a Function at the Convergence Point of Its Spectral Expansion Associated with B-Elliptic Operators
Sh. A. AlimovNational University of Uzbekistan, Faculty of Mathematics, 100174, Tashkent, UzbekistanSh. T. PirmatovTashkent State Technical University, Faculty of Mechanical Engineering, 100095, Tashkent, Uzbekistan
ABI
Аннотация
In this paper, the necessary conditions for summability of spectral expansions in eigenfunctions of the Bessel type singular elliptic operator are studied in an arbitrary $$N$$ -dimensional domain. It is proved that if the spectral expansion of an arbitrary function at some point is summed by Riesz means, then its mean value over the hemisphere at the specified point has generalized continuity.
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