In this article, we establish theory of Parseval framelets associated to generalized
multiresolution analysis (GMRA) in the setting of reducing subspace for the local field of …

A constructive algorithm based on the theory of spectral pairs for constructing nonuniform
wavelet basis in L 2 (ℝ) L^2(\mathbbR) was considered by Gabardo and Nashed (J Funct …

In this paper, we present a unified approach to the study of shift-invariant systems to be
frames on local fields of positive characteristic. We establish a necessary condition and …

Nonuniform nonhomogeneous dual wavelet frames in Sobolev spaces in $$L^2({\mathbb {K}})$$
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In real life applications not all signals are obtained by uniform shifts; so there is a natural
question regarding analysis and decompositions of these types of signals by a stable …

The theory of Gabor systems and of their frame properties is available on any locally
compact abelian (LCA) group [23]. However, the construction of explicit examples of Gabor …

Time-frequency analysis of signals had its origin almost 60 years ago, there have been
major developments of the time-scale and time-frequency analysis approach in the last few …

In this paper, we introduce the notion of nonhomogeneous dual wavelet frames in Sobolev
spaces over local fields. We provide the complete characterization of nonhomogeneous …

Tight wavelet frames are different from the orthonormal wavelets because of redundancy. By
sacrificing orthonormality and allowing redundancy, the tight wavelet frames become much …

Wavelet frames are different from the orthonormal wavelets because of redundancy. By
sacrificing orthonormality and allowing redundancy, wavelet frames become much easier to …