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Article Dans Une Revue Journal of Noncommutative Geometry Année : 2008

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

Résumé

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.

Dates et versions

hal-00366551 , version 1 (09-03-2009)

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Victor Gayral, Jose M. Gracia-Bondia, Joseph C. Varilly. Fourier analysis on the affine group, quantization and noncompact Connes geometries. Journal of Noncommutative Geometry, 2008, 2 (2), pp.215-261. ⟨10.4171/JNCG/20⟩. ⟨hal-00366551⟩
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