Heat Properties for Groups

IF 1.2 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Fourier Analysis and Applications Pub Date : 2024-08-14 DOI:10.1007/s00041-024-10103-0

Erik Bédos, Roberto Conti

引用次数: 0

Abstract

We revisit Fourier’s approach to solve the heat equation on the circle in the context of (twisted) reduced group C*-algebras, convergence of Fourier series and semigroups associated to negative definite functions. We introduce some heat properties for countably infinite groups and investigate when they are satisfied. Kazhdan’s property (T) is an obstruction to the weakest property, and our findings leave open the possibility that this might be the only one. On the other hand, many groups with the Haagerup property satisfy the strongest version. We show that this heat property implies that the associated heat problem has a unique solution regardless of the choice of the initial datum.

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组的热性能

我们结合（扭曲）还原群 C* 玻钎、傅里叶级数的收敛性以及与负定函数相关的半群，重温了傅里叶求解圆上热方程的方法。我们介绍了可数无限群的一些热性质，并研究了它们何时满足。卡兹丹性质（T）是最弱性质的障碍，而我们的发现为这可能是唯一的性质提供了可能性。另一方面，许多具有哈格鲁普性质的群都满足最强性质。我们证明，无论初始基准如何选择，这一热性质都意味着相关的热问题有唯一的解。

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 Fourier Analysis and Applications 数学-应用数学

CiteScore

2.10

自引率

16.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Fourier Analysis and Applications will publish results in Fourier analysis, as well as applicable mathematics having a significant Fourier analytic component. Appropriate manuscripts at the highest research level will be accepted for publication. Because of the extensive, intricate, and fundamental relationship between Fourier analysis and so many other subjects, selected and readable surveys will also be published. These surveys will include historical articles, research tutorials, and expositions of specific topics. TheJournal of Fourier Analysis and Applications will provide a perspective and means for centralizing and disseminating new information from the vantage point of Fourier analysis. The breadth of Fourier analysis and diversity of its applicability require that each paper should contain a clear and motivated introduction, which is accessible to all of our readers. Areas of applications include the following: antenna theory * crystallography * fast algorithms * Gabor theory and applications * image processing * number theory * optics * partial differential equations * prediction theory * radar applications * sampling theory * spectral estimation * speech processing * stochastic processes * time-frequency analysis * time series * tomography * turbulence * uncertainty principles * wavelet theory and applications