Fourier transforms of spherical distributions on compact symmetric spaces
| dc.creator | Olafsson, Gestur | |
| dc.creator | Schlichtkrull, Henrik | |
| dc.date | 2008-10-01 | |
| dc.date | 2009-04-29 | |
| dc.date.accessioned | 2026-07-07T13:09:12Z | |
| dc.date.available | 2026-07-07T13:09:12Z | |
| dc.description | In our previous articles "A local Paley-Wiener theorem for compact symmetric spaces", Adv. Math. 218 (2008), 202--215, and "Fourier series on compact symmetric spaces" (submitted) we studied Fourier series on a compact symmetric space M=U/K. In particular, we proved a Paley-Wiener type theorem for the smooth functions on M, which have sufficiently small support and are K-invariant, respectively K-finite. In this article we extend those results to K-invariant distributions on M. We show that the Fourier transform of a distribution, which is supported in a sufficiently small ball around the base point, extends to a holomorphic function of exponential type. We describe the image of the Fourier transform in the space of holomorphic functions. We characterize the singular support of a distribution in terms of its Fourier transform. Finally, we use the Paley-Wiener theorem to characterize the distributions of small support, which are in the range of a given invariant differential operator. | |
| dc.description | New version. Our previous results were for symmetric spaces of the compact type. The new version including an appendix sketching the extension of the Paley-Wiener theorem for K-invariant functions and distributions to compact symmetric spaces | |
| dc.identifier | https://arxiv.org/abs/0810.0062 | |
| dc.identifier | http://arxiv.org/abs/0810.0062 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228657 | |
| dc.subject | Functional Analysis | |
| dc.subject | 43A85, 53C35, 22E46 | |
| dc.title | Fourier transforms of spherical distributions on compact symmetric spaces | |
| dc.type | text |