Abstract.
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.
Communicated by Vincent Rivasseau
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Corresponding author
Additional information
Submitted: October 28, 2005; Accepted: February 17, 2006
Rights and permissions
About this article
Cite this article
Burnol, JF. Spacetime Causality in the Study of the Hankel Transform. Ann. Henri Poincaré 7, 1013–1034 (2006). https://doi.org/10.1007/s00023-006-0274-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00023-006-0274-8