## Spherical harmonics and subharmonic functions.(English. Russian original)Zbl 0594.31013

Math. USSR, Sb. 53, 147-167 (1986); translation from Mat. Sb., Nov. Ser. 125(167), No. 2, 147-166 (1984).
According to an idea of L. A. Rubel [Lect. Notes Math. 336, 51-62 (1973; Zbl 0268.30011)], that a Fourier analysis for subharmonic functions in $$R_ m$$ (m$$\geq 3)$$ could be developed, the author tries to prove that this is really possible. He realizes this on the unit sphere in $$R_ m$$, generalizing L. A. Rubel’s and B. A. Taylor’s results for entire and meromorphic functions. He also finds $$R_ m$$ analogues for Bernstein’s, Borel’s and Lindelöf’s classical theorems for entire functions. The paper can be considered as a parallel for subharmonic functions in $$R_ m$$ of Fourier analysis in $$R_ 2$$.
Reviewer: V.Ionescu

### MSC:

 31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions 42C15 General harmonic expansions, frames

### Keywords:

Fourier analysis for subharmonic functions

Zbl 0268.30011
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