Relative Convolutions. I. Properties and Applications
| dc.creator | Kisil, Vladimir V. | |
| dc.date | 1994-10-03 | |
| dc.date | 2004-02-05 | |
| dc.date.accessioned | 2026-07-07T09:02:54Z | |
| dc.date.available | 2026-07-07T09:02:54Z | |
| dc.description | 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. KEYWORDS: Lie groups and algebras, convolution operator, representation theory, Heisenberg group, integral representations, Hardy space, Szegö projector, Toeplitz operators, Fock space, Segal--Bargmann space, Bargmann projector, Dirac equation, Clifford analysis, coherent states, wavelet transform, quantization. | |
| dc.description | 42 pages, LaTeX2e; on 05/02/2004 files was updated to produce PS | |
| dc.identifier | https://arxiv.org/abs/funct-an/9410001 | |
| dc.identifier | http://arxiv.org/abs/funct-an/9410001 | |
| dc.identifier | Adv. Math. 147 (1999), no. 1, 35--73 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/148808 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.title | Relative Convolutions. I. Properties and Applications | |
| dc.type | text |