A RANGE FUNCTION APPROACH TO SHIFT-INVARIANT SPACES ON LOCALLY COMPACT ABELIAN GROUPS

IF 0.9 4区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

International Journal of Wavelets Multiresolution and Information Processing Pub Date : 2010-01-01 DOI:10.1142/S021969131392001X

R. A. Kamyabi Gol, R. R. Tousi, R. Raisi Tousi

引用次数: 10

Abstract

This paper develops several aspects of shift-invariant spaces on locally compact abelian groups. For a second countable locally compact abelian group G we prove a useful Hilbert space isomorphism, introduce range functions and give a characterization of shift-invariant subspaces of L2(G) in terms of range functions. Utilizing these functions, we generalize characterizations of frames and Riesz bases generated by shifts of a countable set of generators from L2(ℝn) to L2(G).

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局部紧阿贝尔群上平移不变空间的极差函数方法

研究了局部紧阿贝尔群上平移不变空间的几个方面。对于第二可数局部紧阿贝尔群G，我们证明了一个有用的Hilbert空间同构，引入了值域函数，给出了L2(G)的平移不变子空间用值域函数的刻画。利用这些函数，我们推广了由L2(n)到L2(G)的可数发生器集的移位所产生的坐标系和Riesz基的刻画。

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

International Journal of Wavelets Multiresolution and Information Processing 工程技术-计算机：软件工程

CiteScore

2.60

自引率

7.10%

发文量

审稿时长

2.7 months

期刊介绍： International Journal of Wavelets, Multiresolution and Information Processing (hereafter referred to as IJWMIP) is a bi-monthly publication for theoretical and applied papers on the current state-of-the-art results of wavelet analysis, multiresolution and information processing. Papers related to the IJWMIP theme are especially solicited, including theories, methodologies, algorithms and emerging applications. Topics of interest of the IJWMIP include, but are not limited to: 1. Wavelets: Wavelets and operator theory Frame and applications Time-frequency analysis and applications Sparse representation and approximation Sampling theory and compressive sensing Wavelet based algorithms and applications 2. Multiresolution: Multiresolution analysis Multiscale approximation Multiresolution image processing and signal processing Multiresolution representations Deep learning and neural networks Machine learning theory, algorithms and applications High dimensional data analysis 3. Information Processing: Data sciences Big data and applications Information theory Information systems and technology Information security Information learning and processing Artificial intelligence and pattern recognition Image/signal processing.