Eur. Phys. J. H 39, 575–589 (2014)
https://doi.org/10.1140/epjh/e2014-50021-1

On the mathematics underlying dispersion relations

University of Mississippi, P.O. Box 1848 University, MS 38677, USA

^a e-mail: cpembert@olemiss.edu

Received: 13 March 2014
Received in final form: 22 September 2014
Published online: 24 October 2014

Abstract

The history of mathematical methods underlying the study of dispersion relations in physics is discussed. In particular, some misconceptions connected with a theorem known in the physics literature as Titchmarsh’s Theorem are addressed. It is pointed out that the aforementioned theorem is a compilation of two well-known theorems in mathematics, the Paley-Wiener theorem and the Marcel Riesz theorem.