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- W2156830809 abstract "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." @default.
- W2156830809 created "2016-06-24" @default.
- W2156830809 creator A5073966020 @default.
- W2156830809 date "2002-04-01" @default.
- W2156830809 modified "2023-09-27" @default.
- W2156830809 title "Spaces of Analytical Functions and Wavelets--Lecture Notes" @default.
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