Zeta Functions

September 18 - 22, 2006, Moscow, Russia

Laboratoire J.-V. Poncelet

General

Announcement

Participants

Practical details

Program

Jean-Francois Burnol

Universite de Lille 1, France

Hilbert spaces, Differential equations, Causality

Some Hilbert spaces of square integrable functions on the positive half-line arise naturally (via the "co-Poisson" formula) in the study of the Riemann, Dirichlet or Dedekind zeta functions. Their equations whose potentials are expressed as Fredholm determinants of the cosine, sine, or Hankel kernels. Among these families of Hilbert spaces, one has been established to be intimately associated with the Klein-Gordon equation in 1+1 dimensions and especially with the Einstein causality property of this hyperbolic equation (for a classical field).