Journal of Lie Theory 34 (2024), No. 2, 353--384
Copyright Heldermann Verlag 2024
A Topological Paley-Wiener-Schwartz Theorem for Sections of Homogeneous Vector Bundles on G/K
Martin Olbrich
Department of Mathematics, FSTM, Université du Luxembourg, Esch-sur-Alzette, Luxembourg
martin.olbrich@uni.lu
Guendalina Palmirotta
Department of Mathematics, FSTM, Université du Luxembourg, Esch-sur-Alzette, Luxembourg
guendalina.palmirotta@uni.lu
We study the Fourier transforms for compactly supported distributional sections of complex homogeneous vector bundles on symmetric spaces of non-compact type X = G/K. We prove a characterization of their range. In fact, from Delorme's Paley-Wiener theorem for compactly supported smooth functions on a real reductive group of Harish-Chandra class, we deduce topological Paley-Wiener and Paley-Wiener-Schwartz theorems for sections.
Keywords: Analysis on symmetric spaces, inhomogeneous vector bundles, invariant differential operators, Paley-Wiener theorems.
MSC: 22E46, 22E30, 58J50.
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