{"publisher":"Heldermann Verlag","date_created":"2026-02-20T20:04:49Z","title":"A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on $G/K$","issue":"2","year":"2022","external_id":{"arxiv":["2202.06905"]},"language":[{"iso":"eng"}],"publication":"Journal of Lie theory","abstract":[{"lang":"eng","text":"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."}],"date_updated":"2026-02-20T20:07:31Z","author":[{"full_name":"Olbrich, Martin","last_name":"Olbrich","first_name":"Martin"},{"first_name":"Guendalina","last_name":"Palmirotta","full_name":"Palmirotta, Guendalina","id":"109467"}],"volume":34,"publication_status":"published","citation":{"bibtex":"@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} }","mla":"Olbrich, Martin, and Guendalina Palmirotta. “A Topological Paley-Wiener-Schwartz Theorem for Sections of Homogeneous Vector Bundles on $G/K$.” <i>Journal of Lie Theory</i>, vol. 34, no. 2, Heldermann Verlag, 2022, pp. 53--384.","short":"M. Olbrich, G. Palmirotta, Journal of Lie Theory 34 (2022) 53--384.","apa":"Olbrich, M., &#38; Palmirotta, G. (2022). A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on $G/K$. <i>Journal of Lie Theory</i>, <i>34</i>(2), 53--384.","ama":"Olbrich M, Palmirotta G. A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on $G/K$. <i>Journal of Lie theory</i>. 2022;34(2):53--384.","chicago":"Olbrich, Martin, and Guendalina Palmirotta. “A Topological Paley-Wiener-Schwartz Theorem for Sections of Homogeneous Vector Bundles on $G/K$.” <i>Journal of Lie Theory</i> 34, no. 2 (2022): 53--384.","ieee":"M. Olbrich and G. Palmirotta, “A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on $G/K$,” <i>Journal of Lie theory</i>, vol. 34, no. 2, pp. 53--384, 2022."},"page":"53--384","intvolume":"        34","_id":"64571","user_id":"109467","department":[{"_id":"10"},{"_id":"548"}],"extern":"1","type":"journal_article","status":"public"}