2018/01/01 by Owais Ahmad, Ahmad, Owais, Firdous A. Shah +1
Computer Science · Mathematics · #11S85 #42C15 #42C40 #43A70 #47A25 #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.1801.00417
openalex publication_date 2018/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Shah and Abdullah [Complex Analysis Operator Theory, 9 (2015), 1589-1608] have introduced a generalized notion of nonuniform multiresolution analysis (NUMRA) on local field K of positive characteristic in which the translation set Λ acting on the scaling function to generate the core space V0 is no longer a group, but is the union of \mathcal Z and a translate of \mathcal Z, given by Λ=\0,u(r)/N \+\mathcal Z, where N ≥ 1 is an integer and r is an odd integer such that r and N are relatively prime, and \mathcal Z=\u(n): n∈\mathbb N0\ is a complete list of distinct cosets of the unit disc \mathfrak D in K+. In this paper, we focus on the extension of nonuniform continuous wavelets to the construction of Jth-stage nonuniform discrete wavelets on local fields. We establish some general characterizations for the Jth-stage nonuniform discrete wavelet systems to be orthornormal bases in L2(Λ). Moreover, we establish a relation between the continuous wavelets of L2(K) and their discrete counterparts of l2(Λ).