与正半线上移位不变量空间相关的帧

Pub Date : 2021-08-01 DOI:10.2478/ausm-2021-0002

O. Ahmad, Mobin Ahmad, Neyaz Ahmad

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引用次数: 1

摘要

摘要本文引入Walsh移不变空间的概念，给出了研究L2(t +)中移不变系统为坐标系的一种统一方法。得到了L2(l +)的Walsh平移不变系统构成坐标系的一个必要条件和三个充分条件。进一步讨论了主要结果的应用，得到了关于正半线上Gabor框架和小波框架的一些已知结论。

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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Frames associated with shift invariant spaces on positive half line

Abstract In this paper, we introduce the notion of Walsh shift-invariant space and present a unified approach to the study of shift-invariant systems to be frames in L2(ℝ+). We obtain a necessary condition and three sufficient conditions under which the Walsh shift-invariant systems constitute frames for L2(ℝ+). Furthermore, we discuss applications of our main results to obtain some known conclusions about the Gabor frames and wavelet frames on positive half line.

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