Analysis in $R^{1,1}$ or the Principal Function Theory
funct-an
2007-05-23 v2 Complex Variables
Functional Analysis
Abstract
We explore a function theory connected with the principal series representation of SL(2,R) in contrast to standard complex analysis connected with the discrete series. We construct counterparts for the Cauchy integral formula, the Hardy space, the Cauchy-Riemann equation and the Taylor expansion. Keywords: Complex analysis, Cauchy integral formula, Hardy space, Taylor expansion, Cauchy-Riemann equations, Dirac operator, group representations, SL(2,R), discrete series, principal series, wavelet transform, coherent states.
Cite
@article{arxiv.funct-an/9712003,
title = {Analysis in $R^{1,1}$ or the Principal Function Theory},
author = {Vladimir V. Kisil},
journal= {arXiv preprint arXiv:funct-an/9712003},
year = {2007}
}
Comments
25 pages, 2 figures. 14/12/97: Language corrections