Analytic families of eigenfunctions on a reductive symmetric space

Abstract

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.

115 pages, LaTeX

References in corpus (1)

• The Plancherel decomposition for a reductive symmetric space II. Representation theory

Cited by in corpus (6)

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• Paley-Wiener spaces for real reductive Lie groups
• Harmonic Analysis on Homogeneous Spaces