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Calculus of operators: covariant transform and relative convolutions. (English) Zbl 1305.43009
The paper is a survey of pseudo-differential and convolution type operators calculi from the point of view of covariant and contravariant transforms and relative convolutions as a part of representation theory. Plenty of illustrative examples are considered.

MSC:
43A80 Analysis on other specific Lie groups
45P05 Integral operators
47B38 Linear operators on function spaces (general)
47G10 Integral operators
22Exx Lie groups
17Bxx Lie algebras and Lie superalgebras
47C10 Linear operators in \({}^*\)-algebras
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