
Journal of Lie Theory 34 (2024), No. 2, 353384 Copyright Heldermann Verlag 2024 A Topological PaleyWienerSchwartz Theorem for Sections of Homogeneous Vector Bundles on G/K Martin Olbrich Department of Mathematics, FSTM, Université du Luxembourg, EschsurAlzette, Luxembourg martin.olbrich@uni.lu Guendalina Palmirotta Department of Mathematics, FSTM, Université du Luxembourg, EschsurAlzette, Luxembourg guendalina.palmirotta@uni.lu We study the Fourier transforms for compactly supported distributional sections of complex homogeneous vector bundles on symmetric spaces of noncompact type X = G/K. We prove a characterization of their range. In fact, from Delorme's PaleyWiener theorem for compactly supported smooth functions on a real reductive group of HarishChandra class, we deduce topological PaleyWiener and PaleyWienerSchwartz theorems for sections. Keywords: Analysis on symmetric spaces, inhomogeneous vector bundles, invariant differential operators, PaleyWiener theorems. MSC: 22E46, 22E30, 58J50. [ Fulltextpdf (241 KB)] for subscribers only. 