Shift-invariant sequences and non-homogeneous dual wavelet frames on local fields

Recent research has increasingly explored the construction of wavelets and frames in function spaces extending beyond standard domains like R R and 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.