A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on $G/K$
M. Olbrich, G. Palmirotta, Journal of Lie Theory 34 (2022) 53--384.
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Author
Olbrich, Martin;
Palmirotta, GuendalinaLibreCat
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Abstract
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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Journal Title
Journal of Lie theory
Volume
34
Issue
2
Page
53--384
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Olbrich M, Palmirotta G. A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on $G/K$. Journal of Lie theory. 2022;34(2):53--384.
Olbrich, M., & Palmirotta, G. (2022). A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on $G/K$. Journal of Lie Theory, 34(2), 53--384.
@article{Olbrich_Palmirotta_2022, title={A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on $G/K$}, volume={34}, number={2}, journal={Journal of Lie theory}, publisher={Heldermann Verlag}, author={Olbrich, Martin and Palmirotta, Guendalina}, year={2022}, pages={53--384} }
Olbrich, Martin, and Guendalina Palmirotta. “A Topological Paley-Wiener-Schwartz Theorem for Sections of Homogeneous Vector Bundles on $G/K$.” Journal of Lie Theory 34, no. 2 (2022): 53--384.
M. Olbrich and G. Palmirotta, “A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on $G/K$,” Journal of Lie theory, vol. 34, no. 2, pp. 53--384, 2022.
Olbrich, Martin, and Guendalina Palmirotta. “A Topological Paley-Wiener-Schwartz Theorem for Sections of Homogeneous Vector Bundles on $G/K$.” Journal of Lie Theory, vol. 34, no. 2, Heldermann Verlag, 2022, pp. 53--384.
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