2020/09/25 by Rosenkranz, Markus, Landsmann, Günter
#13N10 #16W99 #43A25 #68W30 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2009.12198
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.