22 citations · 94 across the 19 of their papers we have counts for
19 papers
On the system of the functions zeta(s)/(s-rho)^k
Jean-François Burnol
The system of the functions zeta(s)/(s-rho)^k is complete and minimal in a certain sub-Hilbert space of the L^2 space of the critical line. We study whether it is also hereditarily…
On some bound and scattering states associated with the cosine kernel
Jean-Francois Burnol
It is explained how to provide self-adjoint operators having scattering states forming a multiplicity one continuum and bound states whose corresponding eigenvalues have an asympto…
Scattering, determinants, hyperfunctions in relation to Gamma(1-s)/Gamma(s)
Jean-Francois Burnol
The method of realizing certain self-reciprocal transforms as (absolute) scattering, previously presented in summarized form in the case of the Fourier cosine and sine transforms,…
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…