ar X iv : f un ct - a n / 94 10 00 1 v 2 5 F eb 2 00 4 RELATIVE CONVOLUTIONS . I PROPERTIES AND APPLICATIONS
نویسنده
چکیده
To study operator algebras with symmetries in a wide sense we introduce a notion of relative convolution operators induced by a Lie algebra. Relative convolutions recover many important classes of operators, which have been already studied (operators of multiplication, usual group convolutions, two-sided convolution etc.) and their different combinations. Basic properties of relative convolutions are given and a connection with usual convolutions is established. Presented examples show that relative convolutions provide us with a base for systematical applications of harmonic analysis to PDO theory, complex and hypercomplex analysis, coherent states, wavelet transform and quantum theory. Date: September 2, 1994. This work was partially supported by CONACYT Project 1821-E9211, Mexico. On leave from the Odessa State University. 1
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تاریخ انتشار 2004