6 papers
The Segal-Bargmann transform for the heat equation associated with root systems
Gestur Olafsson, Henrik Schlichtkrull
We study the heat equation associated to a multiplicity function on a root system, where the corresponding Laplace operator has been defined by Heckman and Opdam. In particular, we…
Paley-Wiener spaces for real reductive Lie groups
E. P. van den Ban, H. Schlichtkrull
We show that Arthur's Paley-Wiener theorem for K-finite compactly supported smooth functions on a real reductive Lie group G of the Harish-Chandra class can be deduced from the Pal…
An uncertainty principle related to the Euclidean motion group
Jens Gerlach Christensen, Henrik Schlichtkrull
We show that a well known uncertainty principle for functions on the circle can be derived from an uncertainty principle for the Euclidean motion group.
The Plancherel decomposition for a reductive symmetric space II. Representation theory
E. P. van den Ban, H. Schlichtkrull
We obtain the Plancherel decomposition for a reductive symmetric space in the sense of representation theory. Our starting point is the Plancherel formula for spherical Schwartz fu…
The Plancherel decomposition for a reductive symmetric space I. Spherical functions
E. P. van den Ban, H. Schlichtkrull
We prove the Plancherel formula for spherical Schwartz functions on a reductive symmetric space. Our starting point is an inversion formula for spherical smooth compactly supported…
Analytic families of eigenfunctions on a reductive symmetric space
E. P. van den Ban, H. Schlichtkrull
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 co…