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Abstract <p>In this paper, subharmonic functions <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11988_2025_5324_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\({v}\)</EquationSource> <!--VestSPGU2570006Naumova-m1--> </InlineEquation> in an unbounded open semiring, the growth of which is determined by the positive, continuous, increasing, and unbounded function γ(<i>r</i>) defined on [0, ∞) (the growth function), have been considered. The spaces of subharmonic functions of finite γ-type are denoted as <i>S</i>(<i>R</i>, γ). In terms of Fourier coefficients, the criterion for belonging of a subharmonic function to the <i>S</i>(<i>R</i>, γ) space has been obtained. In this paper, some of the results by A.A.&#xa0;Kondratyuk, K.G. Malyutin, B.N. Khabibullin, et al. have been extended to the functions defined in unbounded semiring. Transition to an unbounded semiring causes certain difficulties associated with complex behavior functions in a neighborhood of the boundary. Difference from the plane case appears already when obtaining the criteria for belonging of subharmonic function to a specified class.</p>

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Growth of Subharmonic Functions in a Semicircle

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • A. A. Naumova

摘要

Abstract

In this paper, subharmonic functions \({v}\) in an unbounded open semiring, the growth of which is determined by the positive, continuous, increasing, and unbounded function γ(r) defined on [0, ∞) (the growth function), have been considered. The spaces of subharmonic functions of finite γ-type are denoted as S(R, γ). In terms of Fourier coefficients, the criterion for belonging of a subharmonic function to the S(R, γ) space has been obtained. In this paper, some of the results by A.A. Kondratyuk, K.G. Malyutin, B.N. Khabibullin, et al. have been extended to the functions defined in unbounded semiring. Transition to an unbounded semiring causes certain difficulties associated with complex behavior functions in a neighborhood of the boundary. Difference from the plane case appears already when obtaining the criteria for belonging of subharmonic function to a specified class.