Shift-invariant sequences and non-homogeneous dual wavelet frames on local fields
Abstract
Abstract Recent research has increasingly explored the construction of wavelets and frames in function spaces extending beyond standard domains like $\mathbb{R}$ R and $\mathbb{C}$ C . This paper addresses these developments within the context of local fields. We provide comprehensive characterizations of three shift-invariant structures: Bessel sequences, frame sequences, and Parseval frame sequences. Furthermore, we establish equivalence among non-homogeneous dual wavelet frames across different levels and demonstrate that every non-homogeneous dual wavelet frame can derive its corresponding homogeneous counterpart.
Fields of Study & Subjects
Mathematical Analysis and Transform Methods
advanced mathematical theories
Advanced Banach Space Theory
Publication details
- Journal / source
- Journal of Inequalities and Applications
- Volume
- 2026
- Issue
- 1
- Publication date
- 10 February 2026
- Language
- EN