Spherical harmonics and subharmonic functions

A. A. Kondratyuk

Sbornik. Mathematics, Tome 53 (1986) no. 1, pp. 147-167

Résumé

The method of Fourier series for entire and meromorphic functions was developed by Rubel and Taylor. Rubel conjectured that similar results are valid for subharmonic functions in $\mathbf R^m$, $m\geqslant3$, and suggested the use of spherical harmonics. In this paper a positive solution is given to this conjecture. As corollaries, many-dimensional analogues of classical theorems on entire functions due to Weierstrass, Borel and Lindelöf are deduced. Bibliography: 23 titles.

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