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Spacetime causality in the study of the Hankel transform
Jean-Francois Burnol
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…
Two complete and minimal systems associated with the zeros of the Riemann zeta function
Jean-Francois Burnol
We link together three themes which had remained separated so far: the Hilbert space properties of the Riemann zeros, the ``dual Poisson formula'' of Duffin-Weinberger (also named…
On an analytic estimate in the theory of the Riemann Zeta function and a Theorem of Baez-Duarte
Jean-Francois Burnol
We establish a uniform upper estimate for the values of zeta(s)/zeta(s+A), 0<= A, on the critical line (conditionally on the Riemann Hypothesis). We use this to give a variant, pur…
A lower bound in an approximation problem involving the zeros of the Riemann zeta function
Jean-Francois Burnol
We slightly improve the lower bound of Baez-Duarte, Balazard, Landreau and Saias in the Nyman-Beurling formulation of the Riemann Hypothesis as an approximation problem. We constru…
An adelic causality problem related to abelian L-functions
Jean-Francois Burnol
I associate to a global field K a Lax-Phillips scattering which has the property of causality if and only if the Riemann Hypothesis holds for all the abelian L-functions of K. As a…
Scattering for time series with an application to the zeta function of an algebraic curve
Jean-Francois Burnol
I explain how the Lax-Phillips theory can be applied to a purely innovating time series and compute the corresponding scattering function. I then associate such a time series to an…