Wavelet packets and wavelet frame packets on local fields of positive characteristic (Q441939)

Recently, the concepts of multiresolution analysis (MRA) and wavelets have been generalized to local fields [\textit{H. Jiang, D. Li} and \textit{N. Jin}, J. Math. Anal. Appl. 294, No. 2, 523--532 (2004; Zbl 1045.43012); \textit{Yu. Farkov}, Math. Notes 82, No. 6, 843--859 (2007; Zbl 1142.42015); \textit{M. Nacima}, Math. Balk., New Ser. 24, No. 3-4, 275--284 (2010; Zbl 1227.43005); \textit{S. Albeverio, S. Evdokimov} and \textit{M. Skopina}, J. Fourier Anal. Appl. 16, No. 5, 693--714 (2010; Zbl 1202.42059)]. The paper under review extends the concept of MRA to a local field \(K\) of positive characteristic and describes the construction of wavelets within \(L^2(K)\). The wavelet packets associated with such MRAs and the corresponding orthonormal basis in \(L^2(K)\) are constructed. Also, an analogue of the splitting lemma for frames which outlines the construction of wavelet frame packets in this setting is given.