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arxiv 0705.3511 v3 pith:UKYQU3RF submitted 2007-05-24 hep-th math.RT

Fourier analysis on the affine group, quantization and noncompact Connes geometries

Victor Gayral , Jose M. Gracia-Bondia , Joseph C. Varilly This is my paper
classification hep-th math.RT
keywords affinefouriergroupconnesfunctionsnoncompactanalysisconstruction
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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.

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