Complex symplectic geometry with applications to vector differential operators

Abstract

Let l(y) be a formally self-adjoint vector-valued differential expression of order n on an interval (a, \infty)(-\infty \leq a < \infty) with complex matrix-valued function coefficients and finite equal deficiency indices. In this paper, applying complex symplectic algebra, we give a reformulation for self-adjoint domains of the minimal operator associated with l(y) and classify them.