A Topological Paley-Wiener-Schwartz Theorem for Sections of Homogeneous Vector Bundles on G/K

M. Olbrich; G. Palmirotta

doi:10.5802/jolt.1339

M. Olbrich; G. Palmirotta

Journal of Lie Theory, Volume 34 (2024) no. 2, pp. 353-384

Abstract

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.

arXiv Zbl

DOI: 10.5802/jolt.1339

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

@article{JOLT_2024_34_2_a4,
     author = {M. Olbrich and G. 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},
     number = {2},
     doi = {10.5802/jolt.1339},
     zbl = {1536.22028},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1339/}
}

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M. Olbrich; G. 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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