Nonuniform Multiresolution Analysis on Local Fields of Positive Characteristic

Nonuniform wavelet packets on local fields of positive characteristic

“…Subsequently, tight wavelet frames on local fields of positive characteristic were constructed by Shah and Debnath [21] using extension principles. More results in this direction can also be found in [15][16][17][18] and the references therein.…”

“…Recently, Shah and Abdullah [16] have generalized the concept of multiresolution analysis on Euclidean spaces R n to nonuniform multiresolution analysis on local fields of positive characteristic, in which the translation set acting on the scaling function associated with the multiresolution analysis to generate the subspace V 0 is no longer a group, but is the union of Z and a translate of Z, where Z = {u(n) : n ∈ N 0 } is a complete list of (distinct) coset representation of the unit disc D in the locally compact Abelian group K + . More precisely, this set is of the form Λ = {0, r/N} + Z, where N ≥ 1 is an integer and r is an odd integer such that r and N are relatively prime.…”

On Characterization of Nonuniform Tight Wavelet Frames on Local Fields

“…to be a frame for L 2 (K). These studies were continued by Shah and his colleagues in series of papers [11][12][13][14][15]. Motivated and inspired by the above work, we provide the complete characterization of nonuniform tight wavelet frames on local fields of positive characteristic by means of Fourier transform technique.…”

Dual wavelets associated with nonuniform MRA

“…NUMRA with multiplicity D, is called NUMRA-D that generalizes a particular case of a result of Calogero and Garrigos [3] on biorthogonal MRA's of multiplicity D in nonstandard setup. A study with respect to NUMRA has been done by many authors in the references [8,9,10,11,12,15,16,17].…”