Laboratoire J.-V. Poncelet
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).
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