Geodesic
A Topological Paley-Wiener-Schwartz Theorem for Sections of Homogeneous Vector Bundles on G/K
Martin Olbrich1 ; Guendalina Palmirotta1
1Department of Mathematics, FSTM, Université du Luxembourg, Esch-sur-Alzette, Luxembourg
Journal of Lie Theory, Tome 34 (2024) no. 2, pp. 353-384

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 22E46, 22E30, 58J50
Mots-clés : Analysis on symmetric spaces, inhomogeneous vector bundles, invariant differential operators, Paley-Wiener theorems

Martin Olbrich  1   ; Guendalina Palmirotta  1

1 Department of Mathematics, FSTM, Université du Luxembourg, Esch-sur-Alzette, Luxembourg 
Martin Olbrich; Guendalina Palmirotta. A Topological Paley-Wiener-Schwartz Theorem for Sections of Homogeneous Vector Bundles on G/K. Journal of Lie Theory, Tome 34 (2024) no. 2, pp. 353-384. http://geodesic.mathdoc.fr/item/JOLT_2024_34_2_a4/
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     author = {Martin Olbrich and Guendalina Palmirotta},
     title = {A {Topological} {Paley-Wiener-Schwartz} {Theorem} for {Sections} of {Homogeneous} {Vector} {Bundles} on {G/K}},
     journal = {Journal of Lie Theory},
     pages = {353--384},
     year = {2024},
     volume = {34},
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     url = {http://geodesic.mathdoc.fr/item/JOLT_2024_34_2_a4/}
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