Rocky Mountain Journal of Mathematics
- Rocky Mountain J. Math.
- Volume 49, Number 1 (2019), 79-99.
Galois wavelet transforms over finite fields
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.
Rocky Mountain J. Math., Volume 49, Number 1 (2019), 79-99.
First available in Project Euclid: 10 March 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 12E20: Finite fields (field-theoretic aspects) 42C40: Wavelets and other special systems
Secondary: 12F10: Separable extensions, Galois theory 13B05: Galois theory 20G40: Linear algebraic groups over finite fields 81R05: Finite-dimensional groups and algebras motivated by physics and their representations [See also 20C35, 22E70]
Farashahi, Arash Ghaani. Galois wavelet transforms over finite fields. Rocky Mountain J. Math. 49 (2019), no. 1, 79--99. doi:10.1216/RMJ-2019-49-1-79. https://projecteuclid.org/euclid.rmjm/1552186953