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Abstract <p>This paper considers spaces of delta-subharmonic functions on an open unbounded semiring. We introduce a definition of a delta-subharmonic function of finite <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\gamma \)</EquationSource> <!--RusMath2670017Naumova-m1--> </InlineEquation>-growth on an unbounded semiring in which no restrictions are imposed on the growth function. We obtain criteria for a delta-subharmonic function to belong to this space, which are formulated in terms of the Fourier coefficients of this function. The criteria extend to the semiring the results obtained earlier in a joint work by Rubel and Taylor for meromorphic functions on the complex plane and the results of Malyutin for delta-subharmonic functions on the half-plane.</p>

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On the Growth of Delta-Subharmonic Functions on an Unbounded Semiring

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • A. A. Naumova

摘要

Abstract

This paper considers spaces of delta-subharmonic functions on an open unbounded semiring. We introduce a definition of a delta-subharmonic function of finite \(\gamma \) -growth on an unbounded semiring in which no restrictions are imposed on the growth function. We obtain criteria for a delta-subharmonic function to belong to this space, which are formulated in terms of the Fourier coefficients of this function. The criteria extend to the semiring the results obtained earlier in a joint work by Rubel and Taylor for meromorphic functions on the complex plane and the results of Malyutin for delta-subharmonic functions on the half-plane.