A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on G/K

English

Palmirotta, Guendalina[University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]

Olbrich, Martin[University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]

2022

Yes

[en] We study the Fourier transform for compactly supported distributional sections of complex homogeneous vector bundles on symmetric spaces of non-compact type X = G/K. We prove a characterisation 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.