Holomorphic harmonic analysis on complex reductive groups

Details Holomorphic harmonic analysis on complex reductive groups Holomorphic harmonic analysis on complex reductive groups

2007-09-04

arxiv.org/abs/0709.0510v1

Mathematics

Group Theory

15 pages, revision of a preprint by the first author in 2001

Scientific paper

We define the holomorphic Fourier transform of holomorphic functions on complex reductive groups, prove some properties like the Fourier inversion formula, and give some applications. The definition of the holomorphic Fourier transform makes use of the notion of $K$-admissible measures. We prove that $K$-admissible measures are abundant, and the definition of holomorphic Fourier transform is independent of the choice of $K$-admissible measures.

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