A new splitting trick for wavelet packets on local fields of positive characteristic (Q2825729)

In the paper, a construction of wavelet packets on local fields with positive characteristic is presented. The novelty with respect to other approaches is that the wavelet subspaces are splitted directly without using low-pass and high-pass filters associated with multiresolution analysis. This method also overcomes the difficulty of constructing non-orthogonal wavelet packets with dilation factor different from~\(2\). It is proven that the wavelet packets generate a Riesz basis for \(L^2(K)\).NEWLINENEWLINEThe paper is well-organized, it contains an interesting introduction and numerous literature hints. Necessary notions are introduced and explained, the proofs are clear. Linguistic mistakes disturb fluent reading.