Spaces of Analytical Functions and Wavelets--Lecture Notes
| dc.creator | Kisil, Vladimir V. | |
| dc.date | 2002-04-01 | |
| dc.date.accessioned | 2026-07-07T04:47:22Z | |
| dc.date.available | 2026-07-07T04:47:22Z | |
| dc.description | This is (raw) lecture notes of the course read on 6th European intensive course on Complex Analysis (Coimbra, Portugal) in 2000. Our purpose is to describe a general framework for generalizations of the complex analysis. As a consequence a classification scheme for different generalizations is obtained. The framework is based on wavelets (coherent states) in Banach spaces generated by ``admissible'' group representations. Reduced wavelet transform allows naturally describe in abstract term main objects of an analytical function theory: the Cauchy integral formula, the Hardy and Bergman spaces, the Cauchy-Riemann equation, and the Taylor expansion. Among considered examples are classical analytical function theories (one complex variables, several complex variables, Clifford analysis, Segal-Bargmann space) as well as new function theories which were developed within our framework (function theory of hyperbolic type, Clifford version of Segal-Bargmann space). We also briefly discuss applications to the operator theory (functional calculus) and quantum mechanics. | |
| dc.description | LaTeX, pages 92, two PS picture | |
| dc.identifier | https://arxiv.org/abs/math/0204018 | |
| dc.identifier | http://arxiv.org/abs/math/0204018 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63689 | |
| dc.subject | Complex Variables | |
| dc.subject | Mathematical Physics | |
| dc.subject | Functional Analysis | |
| dc.subject | 30G30, 42C40, 43A85, 46H30, 47A13, 81R30, 81R60 | |
| dc.title | Spaces of Analytical Functions and Wavelets--Lecture Notes | |
| dc.type | text |