Analysis in $R^{1,1}$ or the Principal Function Theory

Details Analysis in $R^{1,1}$ or the Principal Function Theory Analysis in $R^{1,1}$ or the Principal Function Theory

1997-12-09

arxiv.org/abs/funct-an/9712003v2

Complex Variables Theory Appl., 40(1999), no.2, pp. 93--118

Mathematics

Complex Variables

25 pages, 2 figures. 14/12/97: Language corrections

Scientific paper

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.

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