An Algebraic Approach to Fourier Transformation
Rings and Algebras
2021-07-01 v3
Abstract
The notion of Fourier transformation is described from an algebraic perspective that lends itself to applications in Symbolic Computation. We build the algebraic structures on the basis of a given Heisenberg group (in the general sense of nilquadratic groups enjoying a splitting property); this includes in particular the whole gamut of Pontryagin duality. The free objects in the corresponding categories are determined, and various examples are given. As a first step towards Symbolic Computation, we study two constructive examples in some detail -- the Gaussians (with and without polynomial factors) and the hyperbolic secant algebra.
Keywords
Cite
@article{arxiv.2009.12198,
title = {An Algebraic Approach to Fourier Transformation},
author = {Markus Rosenkranz and Günter Landsmann},
journal= {arXiv preprint arXiv:2009.12198},
year = {2021}
}
Comments
127 pages, 1 figure