 94305 Vladimir V. Kisil, CINVESTAV del IPN (Mexico) and
 Relative Convolutions. I
Properties and Applications
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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, twosided 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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