仿射群、量子化和非紧Connes几何的Fourier分析
Fourier analysis on the affine group, quantization and noncompact Connes geometries
摘要：
我们发现的Stratonovich-Weyl量化的nonunimodular仿射群的线。由此得到半平面上函数的非交换乘积，它是Connes意义下的非紧谱三元组的基础，相应的Wigner函数再现了信号处理的时频分布。同样的构造导致仿射群上的标量傅里叶变换，简化和扩展了基里洛夫提出的傅里叶变换。
英文摘要：
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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