Shift-invariant sequences and non-homogeneous dual wavelet frames on local fields
Year: 2026
Type: article
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.
Authors: Jianping Zhang, Yungang Jiao, Kepu Li
Institution: Yan'an University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,190
OpenAlex ID: W7128484128