94-305 Vladimir V. Kisil, CINVESTAV del IPN (Mexico) and

Relative Convolutions. I Properties and Applications (102K, LaTeX2e) Oct 3, 94

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Abstract. To study operator algebras with symmetries in a wide sense we introduce a notion of {\em 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.

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