Construction of Nonuniform Wavelet Frames on Non-Archimedean Fields

Ahmad, Owais; Ahmad, Neyaz

doi:10.1007/s11040-020-09371-1

Cited by 10 publications

(3 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They call this a nonuniform multiresolution analysis on local fields of positive characteristic.The notion of nonuniform wavelet frames on non-Archimedean local fields was introduced by Ahmad and Sheikh [12] and established a complete characterization of tight nonuniform wavelet frames on non-Archimedean local fields. More results in this direction can also be found in [1,2,3,4,5,6,7,8,9,10,11,13,41,48,49] and the references therein.…”

Section: Introductionmentioning

confidence: 68%

Nonuniform low-pass filters on non Archimedean local fields

Ahmad

Wani

Hazari

et al. 2021

J. Numer. Anal. Approx. Theory

Self Cite

View full text Add to dashboard Cite

In real life application all signals are not obtained from uniform shifts; so there is a natural question regarding analysis and decompositions of this types of signals by a stable mathematical tool. Gabardo and Nashed (J. Funct. Anal. 158:209-241, 1998) filled this gap by the concept of nonuniform multiresolution analysis. In this setting, the associated translation set \(\Lambda =\left\{ 0,r/N\right\}+2\,\mathbb Z\) is no longer a discrete subgroup of \(\mathbb R\) but a spectrum associated with a certain one-dimensional spectral pair and the associated dilation is an even positive integer related to the given spectral pair. The main aim of this article is to provide the characterization of nonuniform low-pass filters on non-Archimedean local fields.

show abstract

Section: Introductionmentioning

confidence: 68%

Nonuniform low-pass filters on non Archimedean local fields

Ahmad

Wani

Hazari

et al. 2021

J. Numer. Anal. Approx. Theory

Self Cite

View full text Add to dashboard Cite

show abstract

“…Jiang et al [18] pointed out a method for constructing orthogonal wavelets on local field K with a constant generating sequence and derived necessary and sufficient conditions for a solution of the refinement equation to generate a multiresolution analysis of L 2 (K). In the series of papers [1,2,3,4,5,6,7,8,30,31,32,33], we have obtained various results related to wavelet and Gabor frames on local fields.…”

Section: Introductionmentioning

confidence: 99%

Wavelet bi-frames on local fields

Ahmad

2022

J. Numer. Anal. Approx. Theory

Self Cite

View full text Add to dashboard Cite

show abstract

“…Jiang et al [18] pointed out a method for constructing orthogonal wavelets on local field K with a constant generating sequence and derived necessary and sufficient conditions for a solution of the refinement equation to generate a multiresolution analysis of L 2 (K). In the series of papers [1][2][3][4][5][6][7][8][29][30][31][32], we have obtained various results related to wavelet and Gabor frames on local fields.…”

Section: Introductionmentioning

confidence: 99%

Frame multiresolution analysis in discrete settings on local fields of positive characteristic

Ahmad¹,

Sheikh²,

Ahmadini³

et al. 2021

Eur. J. Math. Appl.

View full text Add to dashboard Cite

The main aim of this paper is to develop the theory of frame multiresolution analysis (FMRA) in frequency domain on local field of positive characteristic. We first introduce the notion of shift-invariant subspace and the various characteristics of closed shift-invariant subspaces by their fibres in the frequency domain. We define the frame multiresolution analysis in discrete settings on local fields of positive characteristic (LPFC). Furthermore, we established the properties of multiresolution subspaces, which will provide the quantitative criteria for the construction of FMRAs. We also show that the scaling property of an FMRA also holds for the wavelet subspaces and that the Hilbert space L 2 (K) can be decomposed into the orthogonal sum of these wavelet subspaces.

show abstract

Construction of Nonuniform Wavelet Frames on Non-Archimedean Fields

Cited by 10 publications

References 39 publications

Nonuniform low-pass filters on non Archimedean local fields

Nonuniform low-pass filters on non Archimedean local fields

Wavelet bi-frames on local fields

Frame multiresolution analysis in discrete settings on local fields of positive characteristic

Contact Info

Product

Resources

About