Analytic families of eigenfunctions on a reductive symmetric space

E. P. van den Ban, H. Schlichtkrull

Published 2001-04-04Version 1

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.