紧算子的熵及其在Landau-Pollak-Slepian理论和Sobolev空间中的应用

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Applied and Computational Harmonic Analysis Pub Date : 2025-03-21 DOI:10.1016/j.acha.2025.101762

Thomas Allard, Helmut Bölcskei

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引用次数: 0

摘要

我们导出了紧算子的熵与其特征值之间的一个精确的一般关系。然后展示了如何将这一结果与基本原理一起应用于大大改进最著名的Landau-Pollak-Slepian算子熵的表征和Sobolev空间中单位球的度量熵。

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Entropy of compact operators with applications to Landau-Pollak-Slepian theory and Sobolev spaces

We derive a precise general relation between the entropy of a compact operator and its eigenvalues. It is then shown how this result along with the underlying philosophy can be applied to improve substantially on the best known characterizations of the entropy of the Landau-Pollak-Slepian operator and the metric entropy of unit balls in Sobolev spaces.

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来源期刊

Applied and Computational Harmonic Analysis 物理-物理：数学物理

CiteScore

5.40

自引率

4.00%

发文量

审稿时长

22.9 weeks

期刊介绍： Applied and Computational Harmonic Analysis (ACHA) is an interdisciplinary journal that publishes high-quality papers in all areas of mathematical sciences related to the applied and computational aspects of harmonic analysis, with special emphasis on innovative theoretical development, methods, and algorithms, for information processing, manipulation, understanding, and so forth. The objectives of the journal are to chronicle the important publications in the rapidly growing field of data representation and analysis, to stimulate research in relevant interdisciplinary areas, and to provide a common link among mathematical, physical, and life scientists, as well as engineers.