Spherical harmonics and subharmonic functions

Abstract

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 Rm, m > 3. 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. © 1986 American Mathematical Society.