On a de Branges space related to the Riemann zeta function

Abstract

In a recent article by V.V. Kapustin a de Branges space, whose element is an expression containing the Riemann xi function, was constructed; the canonical system with a diagonal Hamiltonian and the generalized Fourier transform corresponding to the space were found. In this article we present a similar de Branges space with some preferred modifications and we provide formulas related to it; we also write down the Hamiltonian and the generalized Fourier transform.