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JOURNALS // Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry] // Archive

Zh. Mat. Fiz. Anal. Geom., 2005 Volume 1, Number 2, Pages 209–224 (Mi jmag13)

This article is cited in 2 papers

Subharmonic almost periodic functions

A. V. Rakhnin, S. Yu. Favorov

Department of Mechanics and Mathematics, V.N. Karazin Kharkov National University, 4 Svobody Sq., Kharkov, 61077, Ukraine

Abstract: We prove that almost periodicity in the sense of distributions coincides with almost periodicity with respect to Stepanov's metric for the class of subharmonic functions in a strip $z\in\mathbb C:a<\mathrm{Im}\,z<b\}$. We also prove that Fourier coefficients of these functions are continuous functions in Imz. Further, if the logarithm of a subharmonic almost periodic function is a subharmonic function, then it is almost periodic.

Key words and phrases: subharmonic functions, almost periodic functions in the sense of distributions, Fourier coefficients.

MSC: 42A75, 30B50

Received: 21.01.2005

Language: English



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