In this article, we introduce the abstract notion of Galois wavelet groups over finite fields as the finite group of Galois dilations, and translations. We then present a unified theoretical linear algebra approach to the theory of Galois wavelet transforms over finite fields. It is shown that each vector defined over a finite field can be represented as a finite coherent sum of Galois wavelet coefficients as well.
"Galois wavelet transforms over finite fields." Rocky Mountain J. Math. 49 (1) 79 - 99, 2019. https://doi.org/10.1216/RMJ-2019-49-1-79