带分离变量的次谐函数及其与广义凸函数的联系

IF 0.5 Q3 MATHEMATICS

Russian Mathematics Pub Date : 2024-09-05 DOI:10.3103/s1066369x24700439

R. R. Muryasov

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引用次数: 0

摘要

摘要在本文中，我们考虑了在直角坐标系或极坐标系中平面域内可表示为两个一变量函数乘积的二变量函数的次谐波性的必要和充分条件。我们将这些函数与二阶线性微分方程解的凸函数（即两个函数的凸函数）联系起来。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Subharmonic Functions with Separated Variables and Their Connection with Generalized Convex Functions

Abstract

In this paper, we consider the necessary and sufficient conditions for the subharmonicity of functions of two variables representable as a product of two functions of one variable in the Cartesian coordinate system or in the polar coordinate system in domains on the plane. We establish a connection of such functions with functions that are convex with respect to solutions of second-order linear differential equations, that is, convex with respect to two functions.

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来源期刊

Russian Mathematics MATHEMATICS-

CiteScore

0.90

自引率

25.00%

发文量

期刊介绍： Russian Mathematics is a peer reviewed periodical that encompasses the most significant research in both pure and applied mathematics.