Abstract
We consider spectral expansions associated with a self-adjoint extension of the Laplace operator in the n-dimensional domain. We show that if the spectral expansion of an arbitrary function at some point is summable by Riesz means, then its mean value over the sphere with center at that point has certain smoothness.
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Original Russian Text © Sh.A. Alimov, 2012, published in Differentsial’nye Uravneniya, 2012, Vol. 48, No. 4, pp. 498–508.
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Alimov, S.A. On the smoothness of mean values of functions with summable spectral expansion. Diff Equat 48, 506–516 (2012). https://doi.org/10.1134/S0012266112040052
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DOI: https://doi.org/10.1134/S0012266112040052