Method of similar operators in spectral analysis of a fourth-order nonself-adjoint operator

Abstract

We carry out spectral analysis of a nonself-adjoint fourth-order differential operator L defined on the Hilbert space L2[0, 1] by Dirichlet type boundary conditions. We obtain results on the asymptotics of the spectrum of this operator and present equiconvergence estimates for spectral expansions. We show that the operator — L is the generator of an analytic operator semigroup.