Frames associated with shift invariant spaces on positive half line-Reference-Cited by-同舟云学术

Frames associated with shift invariant spaces on positive half line

Published:2021-08-01 Issue:1 Volume:13 Page:23-44
ISSN:2066-7752
Container-title:Acta Universitatis Sapientiae, Mathematica
language:en
Short-container-title:

Author:

Ahmad Owais¹,Ahmad Mobin²,Ahmad Neyaz¹

Affiliation:

1. Department of Mathematics , National Institute of Technology , Srinagar-190006, Jammu and Kashmir , India

2. Department of Mathematics, Faculty of Science , Jazan University , Jazan -45142 , Saudi Arabia

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.sciendo.com/pdf/10.2478/ausm-2021-0002

Reference28 articles.

1. [1] Abdullah, Affine and quasi-sffine frames on positive half line, J. Math. Ext., 10 (3) (2016), 47–61.

2. [2] A. Ahmadi, A. A. Hemmat and R. R. Tousi, Shift-invariant spaces for local fields, Int. J. Wavelets Multiresolut. Inf. Process., 9 (3) (2011), 417–426.

3. [3] S. Albeverio, S. Evdokimov, M. Skopina, p-adic multiresolution analysis and wavelet frames, J. Fourier Anal. Appl., 16 (2010), 693–714.

4. [4] A. Aldroubi, C. Cabrelli, C. Heil, K. Kornelson and U. Molter, Invariance of a shift-invariant space, J. Fourier Anal. Appl., 16 (2010), 60–75.

5. [5] M. Anastasio, C. Cabrelli and V. Paternostro, Extra invariance of shift-invariant spaces on LCA groups, J. Math. Anal. Appl., 370 (2010), 530–537.