Banach Journal of Mathematical Analysis

Calculus of Operators: Covariant Transform and Relative Convolutions

Vladimir V. Kisil

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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.

Article information

Source
Banach J. Math. Anal., Volume 8, Number 2 (2014), 156-184.

Dates
First available in Project Euclid: 4 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1396640061

Digital Object Identifier
doi:10.15352/bjma/1396640061

Mathematical Reviews number (MathSciNet)
MR3189548

Zentralblatt MATH identifier
1305.43009

Subjects
Primary: 45P05: Integral operators [See also 47B38, 47G10]
Secondary: 43A80: Analysis on other specific Lie groups [See also 22Exx] 22E60: Lie algebras of Lie groups {For the algebraic theory of Lie algebras, see 17Bxx} 47C10: Operators in $^*$-algebras

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

Citation

Kisil, Vladimir V. Calculus of Operators: Covariant Transform and Relative Convolutions. Banach J. Math. Anal. 8 (2014), no. 2, 156--184. doi:10.15352/bjma/1396640061. https://projecteuclid.org/euclid.bjma/1396640061


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