Periodic Wavelet Frames on Local Fields of Positive Characteristic. (2nd February 2016)

• Record Type: Journal Article
• Authors: Shah, Firdous A.
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 5(2016)
• Page Start: 603
• Page End: 627
• Publication Date: 2016-02-02
• Subjects: Dual frame -- extension principles -- Fourier transform -- local field -- periodic wavelet frame -- scaling function -- wavelet mask; 42C40 -- 42C15 -- 43A70 -- 11S85; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1144069
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: Periodic wavelet frames have gained considerable popularity in recent years, primarily due to their substantiated applications in diverse and widespread fields of science and engineering. In this article, we introduce the concept of periodic wavelet frame on local fields of positive characteristic and show that under weaker conditions the periodization of any wavelet frame constructed by the unitary extension principle with dilation factor 𝔭 −1 is a periodic wavelet frame on local fields. Moreover, based on the mixed extension principle and Fourier-based techniques of the wavelet frames, we present an explicit method for a pair of dual periodic wavelet frames on local fields of positive characteristic.