Wavelet packets and wavelet frame packets on local fields of positive characteristic

Using a prime element of a local field K of positive characteristic, the concepts of multiresolution analysis (MRA) and wavelets can be generalized to such a field. We prove a version of the splitting lemma for this setup and using this lemma we construct the wavelet packets associated with such MRAs. We show that these wavelet packets generate an orthonormal basis by translations only. We also prove an analogue of the splitting lemma for frames and construct the wavelet frame packets in this setting.