This article is cited in 1 paper

Subharmonic functions with separated variables and their connection with generalized convex functions

R. R. Muryasov

Institute of Mathematics with Computing Centre --- Subdivision of the Ufa Federal Research Centre of Russian Academy of Science, 112 Chernyshevskogo str., Ufa, 450008 Russia

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, i.e., convex with respect to two functions.

Keywords: subharmonic function, generalized derivative, distribution, convex function, differential operator, generalized convex function.

UDC: 517.574: 517.926: 517.927

Received: 24.04.2023
Revised: 05.07.2023
Accepted: 26.09.2023

DOI: 10.26907/0021-3446-2024-6-49-67

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2024, 68:6, 42–57