The generalized Łojasiewicz inequality for definable and subanalytic multifunctions

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2024-10-18 DOI:10.1016/j.jmaa.2024.128977

Michał Kosiba

引用次数: 0

Abstract

This paper is devoted to obtaining the Łojasiewicz inequality (version for two functions), in both the definable and subanalytic cases, under the most relaxed assumptions. It means that we drop the usual continuity and compactness assumptions. In the second part of the paper we concentrate on the Łojasiewicz inequality for multifunctions and apply it to the natural multifunctions related to the medial axis of a set (basic notion in pattern recognition).

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可定义多重函数和亚解析多重函数的广义罗亚斯维兹不等式

本文致力于在最宽松的假设条件下，在可定义和亚解析的情况下，获得 Łojasiewicz 不等式（两个函数的版本）。这意味着我们放弃了通常的连续性和紧凑性假设。在本文的第二部分，我们将集中讨论多重函数的 Łojasiewicz 不等式，并将其应用于与集合中轴相关的自然多重函数（模式识别中的基本概念）。

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

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.