An Algebraic Approach to Fourier Transformation
arXiv:2009.12198
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.
127 pages, 1 figure
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