Finding Hamiltonians satisfying initial values arising from the Riemann zeta-function

Abstract

The general topic of this thesis is the so-called inverse problem in the theory of canonical systems: Given initial values depending on the complex parameter, does there exist a canonical system with a solution (depending on the complex parameter) that satisfies those initial values? As recent (2020) works of Masatoshi Suzuki show, the Riemann hypothesis holds true if the inverse problem can be solved for certain initial values arising from the Riemann zeta-function and if the solution satisfies a certain boundary condition, and that, omitting this boundary condition and slightly restricting the domain of the complex parameter, the inverse problem arising from the Riemann zeta function can be solved. Elaborating the proof (including all the necessary preliminary work) of this result is the main purpose of this thesis.