ON MULTIPLE COMPLETENESS OF A SYSTEM OF EIGEN AND ADJOINT ELEMENTS OF OPERATOR SHEAF IN HILBERT SPACES

In this paper the conditions of the existence of multiple completeness of a system of eigen and adjoint elements of operator sheaf quadratically depending on the spectral parameter in Hilbert space is given.

On Multiple Completeness of the Root Functions of Ordinary Differential Polynomial Pencil with Constant Coefficients

In the space of square integrable functions on a finite segment we consider a class of polynomial pencils of nth-order ordinary differential operators with constant coefficients and two-point boundary-value conditions (at the edges of the segment). We suppose that roots of the characteristic equation of pencils of this class are simple and nonzero. We establish sufficient conditions for m-multiple completeness (1≤m≤n) of the system of root functions of pencils from this class in the space of square integrable functions on this segment.