The Helgason Fourier transform for homogeneous vector bundles over Riemannian symmetric spaces

Roberto Camporesi

Vol. 179 (1997), No. 2, 263–300

DOI: 10.2140/pjm.1997.179.263

Abstract

The Helgason Fourier transform on a noncompact Riemannian symmetric space G∕K is generalized to the homogeneous vector bundles E^τ (τ ∈K) over G∕K. The corresponding inversion formula is obtained by using the Plancherel formula on G and the Subrepresentation Theorem. For radial systems of sections of E^τ, the Helgason Fourier transform reduces to the (operator valued) spherical transform, defined with respect to the (operator valued) τ-spherical functions on G.

Milestones

Received: 13 December 1995

Revised: 7 March 1996

Published: 1 June 1997