On Completeness of Root Vectors of Fourth Order Operator Pencil Corresponding to Eigenvalues of Quarter Plane

摘要

In this paper, we find sufficient conditions for the existence and uniqueness of a regularly holomorphic solution of boundary value problem for a class of fourthorder operator differential equations. Moreover, for an operator pencil associated with the boundary value problem under consideration, we prove the completeness of its root vectors, corresponding to eigenvalues from the sector (S) over tilde (pi/4) = {lambda : vertical bar arg lambda - pi vertical bar < pi/4}. We also establish the completeness of elementary regularly holomorphic solutions of the considered operator differential equation.