Orthonormal bases arising from nilpotent actions

IF 1.2 2区数学 Q1 MATHEMATICS

Transactions of the American Mathematical Society Pub Date : 2023-10-11 DOI:10.1090/tran/9042

Vignon Oussa

引用次数: 0

Abstract

In this paper, we prove the existence of an orthonormal basis in at least one orbit of every generic irreducible representation of a simply connected and connected nilpotent Lie group. Our result has a wide-ranging impact, encompassing all irreducible representations of a nilpotent Lie group that are square-integrable modulo its center. This resolves a fundamental open problem in time-frequency analysis and frame theory, originally posed by Karlheinz Gröchenig. The implications of our findings are significant and far-reaching.

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由幂零作用产生的标准正交基

本文证明了单连通和连通幂零李群的每一个一般不可约表示的至少一个轨道上存在一个标准正交基。我们的结果具有广泛的影响，涵盖了幂零李群的所有不可约表示，这些表示是对其中心进行平方可积的。这解决了Karlheinz Gröchenig最初提出的时频分析和框架理论中的一个基本开放问题。我们的发现意义重大，影响深远。

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

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.