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


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


Zbl 0268.30011
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