Matrix Representation of Magnetic Pseudo-Differential Operators via Tight Gabor Frames

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-04-04 DOI:10.1007/s00041-024-10072-4

Horia D. Cornean, Bernard Helffer, Radu Purice

引用次数: 0

Abstract

In this paper we use some ideas from [12, 13] and consider the description of Hörmander type pseudo-differential operators on \(\mathbb {R}^d\) (\(d\ge 1\)), including the case of the magnetic pseudo-differential operators introduced in [15, 16], with respect to a tight Gabor frame. We show that all these operators can be identified with some infinitely dimensional matrices whose elements are strongly localized near the diagonal. Using this matrix representation, one can give short and elegant proofs to classical results like the Calderón-Vaillancourt theorem and Beals’ commutator criterion, and also establish local trace-class criteria.

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通过紧密 Gabor 框架对磁伪微分算子进行矩阵表示

在本文中，我们使用了 [12, 13] 中的一些观点，并考虑了关于紧 Gabor 框架的 Hörmander 型伪微分算子在 \(\mathbb {R}^d\) (\(d\ge 1\)) 上的描述，包括 [15, 16] 中引入的磁性伪微分算子的情况。我们证明，所有这些算子都可以与一些无限维矩阵相鉴别，这些矩阵的元素在对角线附近强局部化。利用这种矩阵表示，我们可以对卡尔德龙-瓦扬库尔定理和比尔斯换元准则等经典结果给出简短而优雅的证明，还可以建立局部迹类准则。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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