Analytic families of eigenfunctions on a reductive symmetric space

Details Analytic families of eigenfunctions on a reductive symmetric space Analytic families of eigenfunctions on a reductive symmetric space

2001-04-04

arxiv.org/abs/math/0104050v1

Represent. Theory 5 (2001), 615--712 (electronic)

Mathematics

Representation Theory

115 pages, LaTeX

Scientific paper

The asymptotic behavior of holomorphic families of generalized eigenfunctions on a reductive symmetric space is studied. The family parameter is a complex character on the split component of a parabolic subgroup. The main result asserts that the family vanishes if a particular asymptotic coefficient does. This allows an induction of relations between families that will be applied in forthcoming work on the Plancherel and the Paley-Wiener theorem.

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