On the rate of the convergence of the characteristic values of an integral operator associated with a dissipative fourth order differential operator in lim-4 case with finite transmission conditions

Abstract

In this paper, our main aim is to investigate the spectral properties of a singular dissipative fourth order boundary value problem in lim-4 case with finite transmission conditions. For this purpose we construct a suitable differential operator in an appropriate Hilbert space. After showing that this differential operator is a dissipative operator we pass to the resolvent operator with an explicit form. Using this resolvent operator and Krein’s theorem we prove a completeness theorem on the boundary value transmission problem.