Abstract:
A new criterion for completely regular growth of a subharmonic function in $\mathbf R^m$, $m\geqslant3$, is established in terms of spherical harmonics, and a sharp upper bound for the deficiency of such a function is found.
From the expansion of a subharmonic function on the unit sphere $S^m$ in a Fourier–Laplace series the author shows that the function belongs to the space $L^2(S^m)$ for $m=3,4$.
Bibliography: 23 titles.
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