On p-adic tight wavelet frames

We propose a simple method to constructing step mask and corresponding step wavelet functions that generate tight wavelet frames on the field Qp of p-adic numbers. To construct this mask we use three new ideas. First, we consider only an additive group of the field Qp. Second, to construct the mask we use a special tree. Thirdly, we do not use the principle of unitary extension, we use Pontryagin's principle of duality instead. Using this method, we obtain all step refinable functions. (c) 2023 Published by Elsevier Inc.