Zeros of the Riemann zeta function and perturbations of differential operators

A possible approach to the proof of the Riemann hypothesis about zeros of the zeta function consists of constructing a self-adjoint operator whose spectrum coincides with the set of all non-trivial zeta zeros rotated to the real line. In the talk a rank-one perturbation of a self-adjoint operator with the required spectrum will be constructed on a de Branges space. De Branges spaces are widely used for spectral analysis of differential operators, and it will be shown how the result obtained can be transfered to Sturm-Liouville operators.