Dilational symmetries of decomposition and coorbit spaces

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Applied and Computational Harmonic Analysis Pub Date : 2023-11-17 DOI:10.1016/j.acha.2023.101610

Hartmut Führ , Reihaneh Raisi-Tousi

引用次数: 0

Abstract

We investigate the invariance properties of general wavelet coorbit spaces and Besov-type decomposition spaces under dilations by matrices. We show that these matrices can be characterized by quasi-isometry properties with respect to a certain metric in frequency domain. We formulate versions of this phenomenon both for the decomposition and coorbit space settings.

We then apply the general results to a particular class of dilation groups, the so-called shearlet dilation groups. We present a general, algebraic characterization of matrices that are coorbit compatible with a given shearlet dilation group. We explicitly determine the groups of compatible dilations, for a variety of concrete examples.

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分解与共轨道空间的扩张对称性

研究了一般小波共轨空间和besov型分解空间在矩阵扩张下的不变性。我们证明了这些矩阵可以在频域上对某个度规具有准等距性质。我们为分解和共轨空间设置制定了这一现象的版本。然后，我们将一般结果应用于一类特殊的膨胀群，即所谓的shearlet膨胀群。我们提出了与给定shearlet扩张群共轨相容的矩阵的一般代数表征。对于各种具体的例子，我们明确地确定相容膨胀的群。

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

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.