Abstract
AbstractWe construct some class of selfadjoint operators in the Krein spaces consisting of functions on
the straight line $ \{\operatorname{Re}s=\frac{1}{2}\} $.
Each of these operators is a rank-one perturbation of a selfadjoint operator
in the corresponding Hilbert space
and has eigenvalues complex numbers of the form $ \frac{1}{s(1-s)} $,
where $ s $ ranges over the set of nontrivial zeros of the Riemann zeta-function.