Basis properties of root functions of a periodic-antiperiodic fourth order boundary value problem

In this thesis work, it is investigated a fourth order boundary problem. The boundary conditions of this problem are periodic and antiperiodic. These sort of boundary conditions are regular, but not strongly regular. In this work, it is established asymptotic formulae for eigenvalues and eigenfunctions of the considered boundary value problem and proved that the system of root functions forms a basis in certain functional spaces under some conditions.