Elliptic, Parabolic and Hyperbolic Analytic Function Theory--0: Geometry of Domains

Details Elliptic, Parabolic and Hyperbolic Analytic Function Theory--0: Geometry of Domains Elliptic, Parabolic and Hyperbolic Analytic Function Theory--0: Geometry of Domains

2004-10-18

arxiv.org/abs/math/0410399v4

Trans. Inst. Math. of the NAS of Ukraine, v. 1(2004), no.3, pp.100--118

Mathematics

Complex Variables

14 pages, AMS-LaTeX, 31 PS graphcs in 7 Figures; v2--the missing PS file is included now; v3 minor corrections, reference adde

Scientific paper

This paper lays down a foundation for a systematic treatment of three main (elliptic, parabolic and hyperbolic) types of analytic function theory based on the representation theory of SL(2,R) group. We describe here geometries of corresponding domains. The principal role is played by Clifford algebras of matching types. Keywords: analytic function theory, semisimple groups, elliptic, parabolic, hyperbolic, Clifford algebras

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