Abstract:
A new criterion for completely regular growth of a subharmonic function in Rm, m⩾3, 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 Sm in a Fourier–Laplace series the author shows that the function belongs to the space L2(Sm) for m=3,4.
Bibliography: 23 titles.
\Bibitem{Kon81}
\by A.~A.~Kondratyuk
\paper On the method of spherical harmonics for subharmonic functions
\jour Math. USSR-Sb.
\yr 1983
\vol 44
\issue 2
\pages 133--148
\mathnet{http://mi.mathnet.ru/eng/sm2449}
\crossref{https://doi.org/10.1070/SM1983v044n02ABEH000957}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=637858}
\zmath{https://zbmath.org/?q=an:0502.31002|0473.31007}
Linking options:
https://www.mathnet.ru/eng/sm2449
https://doi.org/10.1070/SM1983v044n02ABEH000957
https://www.mathnet.ru/eng/sm/v158/i2/p147
This publication is cited in the following 4 articles:
B. N. Khabibullin, F. B. Khabibullin, “Zeros of Holomorphic Functions in the Unit Ball and Subspherical Functions”, Lobachevskii J Math, 40:5 (2019), 648
B. N. Khabibullin, Z. F. Abdullina, A. P. Rozit, “A uniqueness theorem and subharmonic test functions”, St. Petersburg Math. J., 30:2 (2019), 379–390
B. N. Khabibullin, “A uniqueness theorem for subharmonic functions of finite order”, Math. USSR-Sb., 73:1 (1992), 195–210
A. A. Kondratyuk, “Spherical harmonics and subharmonic functions”, Math. USSR-Sb., 53:1 (1986), 147–167
Citation in format AMSBIB
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