[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.
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Author, co-author :
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)
External co-authors :
A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on G/K