Journal of Lie Theory

no. 2
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, Volume 34 (2024) no. 2, pp. 353-384
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.
DOI: 10.5802/jolt.1339
Classification: 22E46, 22E30, 58J50
Keywords: 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, Volume 34 (2024) no. 2, pp. 353-384. doi: 10.5802/jolt.1339
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     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},
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