With an eye on applications in quantum mechanics and other areas of science, much work has been done to generalize traditional analytic methods to p-adic systems. In 2002 the first paper on p-adic wavelets was published. Since then p-adic wavelet sets, multiresolution analyses, and wavelet frames have all been introduced. However, so far all constructions have involved dilations by p. This paper presents the first construction of a p-adic wavelet system with a more general matrix dilation, laying the foundation for further work in this direction.
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King, E.J., Skopina, M.A. Quincunx multiresolution analysis for L 2(ℚ 22 ). P-Adic Num Ultrametr Anal Appl 2, 222–231 (2010). https://doi.org/10.1134/S2070046610030040