root functions

Multiple Completeness of the Root Functions of the Pencils of Differential Operators with Constant Coefficients and Splitting Boundary Conditions

Authors: Rykhlov V. S.

In the space of square summable functions on the main segment [0,1], the class of polynomial pencils of ordinary differential operators of the n-th order is considered. The coefficients of the differential expression are assumed to be constants. The boundary conditions are assumed to be splitting and two-point at the ends 0 and 1 (l of boundary conditions is taken only at the point 0, and the remaining n − l is taken at the point 1). The differential expression and the boundary forms are assumed to be homogeneous, that is, they contain only main parts.

On Multiple Completeness of the Root Functions of a Certain Class of Pencils of Differential Operators with Constant Coefficients

Authors: Rykhlov V. S., Blinkova O. V.

A polinomial pencil of ordinary differential operators of n-th order generated by a homogeneous differential expression with constant coefficients and by two-point boundary conditions of a special structure with l conditions in zero only (1 ≤ l ≤ n−1) is considered in the space L2[0,1]. The case is studied, when the roots of the characteristic equation lie on a ray coming from the origin.