Convexity and Concavity of \(\boldsymbol f\)-Potentials (Kolmogorov Means)

IF 1.9 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2026-03-27 DOI:10.1134/S1061920825601351

V.I. Bakhtin, N.A. Tsarev

引用次数: 0

Abstract

In the paper, we prove criteria for convexity and concavity of \(f\)-potentials (Kolmogorov means, weighted quasi-arithmetic means), whose particular cases are the arithmetic, geometric, harmonic means, thermodynamic potential (exponential mean), cumulant generating function, and the \(\displaystyle L^{p}\)-norm. Then we compute in quadratures all functions \(f\) satisfying these criteria.

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\(\boldsymbol f\) -势（Kolmogorov均值）的凸性和凹性

本文证明了\(f\) -势（Kolmogorov均值，加权准算术均值）的凸性和凹性判据，其特殊情况是算术、几何、调和均值、热力学势（指数均值）、累积生成函数和\(\displaystyle L^{p}\) -范数。然后在正交中计算满足这些条件的所有函数\(f\)。

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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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.