小波变换的 Donoho-Logan 大筛原理

IF 2.6 2区 数学 Q1 MATHEMATICS, APPLIED
Luís Daniel Abreu , Michael Speckbacher
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引用次数: 0

摘要

在本文中,我们针对哈代空间的小波变换提出了 Donoho 和 Logan 的大筛原理,将最大奈奎斯特密度的概念调整为基础空间的双曲几何。这些结果为 L1 最小化方法提供了确定性保证,并适用于构成哈代空间正交基的一类母小波,而且可以与更高的双曲朗道水平相关联。基函数的显式计算揭示了与 Zernike 多项式的联系。我们为所考虑的空间证明了一个新颖的局部重现公式,并利用它推导出相应小波变换的大筛型集中估计。最后,我们以 Kulikov、Ramos 和 Tilli 基于 Nicola 和 Tilli 的开创性方法所取得的最新成果为基础,讨论了解析情况下的局部最优性和李卜不等式。这导致了小波变换的尖锐不确定性原理和局部利布不等式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Donoho-Logan large sieve principles for the wavelet transform
In this paper we formulate Donoho and Logan's large sieve principle for the wavelet transform on the Hardy space, adapting the concept of maximum Nyquist density to the hyperbolic geometry of the underlying space. The results provide deterministic guarantees for L1-minimization methods and hold for a class of mother wavelets that constitutes an orthonormal basis of the Hardy space and can be associated with higher hyperbolic Landau levels. Explicit calculations of the basis functions reveal a connection with the Zernike polynomials. We prove a novel local reproducing formula for the spaces in consideration and use it to derive concentration estimates of the large sieve type for the corresponding wavelet transforms. We conclude with a discussion of optimality of localization and Lieb inequalities in the analytic case by building on recent results of Kulikov, Ramos and Tilli based on the groundbreaking methods of Nicola and Tilli. This leads to a sharp uncertainty principle and a local Lieb inequality for the wavelet transform.
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来源期刊
Applied and Computational Harmonic Analysis
Applied and Computational Harmonic Analysis 物理-物理:数学物理
CiteScore
5.40
自引率
4.00%
发文量
67
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.
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