Spacetime causality in the study of the Hankel transform
| dc.creator | Burnol, Jean-Francois | |
| dc.date | 2005-09-27 | |
| dc.date | 2006-03-05 | |
| dc.date.accessioned | 2026-07-07T06:43:07Z | |
| dc.date.available | 2026-07-07T06:43:07Z | |
| dc.description | We study Hilbert space aspects of the Klein-Gordon equation in two-dimensional spacetime. We associate to its restriction to a spacelike wedge a scattering from the past light cone to the future light cone, which is then shown to be (essentially) the Hankel transform of order zero. We apply this to give a novel proof, solely based on the causality of this spatio-temporal wave propagation, of the theorem of de Branges and V. Rovnyak concerning Hankel pairs with a support property. We recover their isometric expansion as an application of Riemann's general method for solving Cauchy-Goursat problems of hyperbolic type. | |
| dc.description | 24 pages. Final ms, to appear. Improvements on pages 8 and 9, and 15-16 | |
| dc.identifier | https://arxiv.org/abs/math/0509619 | |
| dc.identifier | http://arxiv.org/abs/math/0509619 | |
| dc.identifier | Ann. Henri Poincaré 7 (2006), 1013--1034 | |
| dc.identifier | doi:10.1007/s00023-006-0274-8 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/102297 | |
| dc.subject | Number Theory | |
| dc.subject | Mathematical Physics | |
| dc.title | Spacetime causality in the study of the Hankel transform | |
| dc.type | text |