Fourier analysis on the affine group, quantization and noncompact Connes geometries
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2008-04
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artículo original
Autores
Gayral, Victor
Gracia Bondía, José M.
Várilly Boyle, Joseph C.
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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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cuantización de Moyal, geometría no conmutativa, transformada de Fourier