A characterization of ( μ , ν ) $(\mu,\nu)$ -dichotomies via admissibility

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2025-06-25 DOI:10.1002/mana.70005

Lucas Backes, Davor Dragičević

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引用次数: 0

Abstract

We present a characterization of $(μ, ν)$ -dichotomies in terms of the admissibility of certain pairs of weighted spaces for nonautonomous discrete time dynamics acting on Banach spaces. Our general framework enables us to treat various settings in which no similar result has been previously obtained as well as to recover and refine several known results. We emphasize that our results hold without any bounded growth assumption and the statements make no use of Lyapunov norms. Moreover, as a consequence of our characterization, we study the robustness of $(μ, ν)$ -dichotomies, that is, we show that this notion persists under small but very general linear perturbations.

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（μ, ν） $(\mu,\nu)$ -二分类的可容许性表征

我们给出了（μ, ν） $(\mu,\nu)$ -二分类在某些加权空间对作用于Banach空间的非自治离散时间动力学的可容许性方面的表征。我们的总体框架使我们能够处理以前没有获得类似结果的各种设置，以及恢复和改进几个已知结果。我们强调我们的结果在没有任何有界增长假设的情况下是成立的，并且这些陈述没有使用李亚普诺夫范数。此外，由于我们的描述，我们研究了（μ, ν） $(\mu, \nu)$ -二分类的鲁棒性，也就是说，我们表明这个概念在小但非常一般的线性扰动下仍然存在。

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

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index