ON A SELF-ADJOINT EXTENSION OF A TYPE OF A MATRIX DIFFERENTIAL OPERATOR.

Abstract

In Coddington and Levinson we get the requisite boundary conditions to be associated with a 2n-th order symmetric differential expression which defines a self-adjoint operator. Naimark2 obtains the corresponding set of boundary conditions to be associated with a 2n x 2n matrix whose elements involve first order derivatives.

Here we discuss self-adjoint extension of certain type of matrix differential operator with a set of non-separated boundary conditions at the end points a, b.

A similar problem associated with an r x r matrix differential operator with elements depending upon differential coefficients of orders up to 2n has also been discussed. Finally, we deal with the corresponding singular problem where the interval [a,b] is replaced by [0, oo].