Fourier analysis on the affine group, quantization and noncompact Connes geometries
High Energy Physics - Theory
2010-11-19 v3 Representation Theory
Abstract
We find the Stratonovich-Weyl quantizer for the nonunimodular affine group of the line. A noncommutative product of functions on the half-plane, underlying a noncompact spectral triple in the sense of Connes, is obtained from it. The corresponding Wigner functions reproduce the time-frequency distributions of signal processing. The same construction leads to scalar Fourier transformations on the affine group, simplifying and extending the Fourier transformation proposed by Kirillov.
Keywords
Cite
@article{arxiv.0705.3511,
title = {Fourier analysis on the affine group, quantization and noncompact Connes geometries},
author = {Victor Gayral and Jose M. Gracia-Bondia and Joseph C. Varilly},
journal= {arXiv preprint arXiv:0705.3511},
year = {2010}
}