Open Access
2014 Calculus of Operators: Covariant Transform and Relative Convolutions
Vladimir V. Kisil
Banach J. Math. Anal. 8(2): 156-184 (2014). DOI: 10.15352/bjma/1396640061

Abstract

The paper outlines a covariant theory of operators related to groups and homogeneous spaces. A methodical use of groups and their representations allows to obtain results of algebraic and analytical nature. The consideration is systematically illustrated by a representative collection of examples.

Citation

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Vladimir V. Kisil. "Calculus of Operators: Covariant Transform and Relative Convolutions." Banach J. Math. Anal. 8 (2) 156 - 184, 2014. https://doi.org/10.15352/bjma/1396640061

Information

Published: 2014
First available in Project Euclid: 4 April 2014

zbMATH: 1305.43009
MathSciNet: MR3189548
Digital Object Identifier: 10.15352/bjma/1396640061

Subjects:
Primary: ‎45P05‎
Secondary: 22E60 , 43A80 , 47C10

Keywords: Berezin symbol , Bergman space , convolution , covariant and contravariant transform , deformation quantization , Fock-Segal-Bargmann (FSB) representation , Heisenberg group, SL , induced representation , Lie groups and algebras , pseudo-differential operators (PDO) , reproducing kernel , singular integral operator(SIO) , Toeplitz operator

Rights: Copyright © 2014 Tusi Mathematical Research Group

Vol.8 • No. 2 • 2014
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