Canonical forms for boundary conditions of self-adjoint differential operators

Abstract

Canonical forms of boundary conditions are important in the study of the eigenvalues of boundary conditions and their numerical computations. The known canonical forms for self-adjoint differential operators, with eigenvalue parameter dependent boundary conditions, are limited to 4-th order differential operators. We derive canonical forms for self-adjoint 2n-th order differential operators with eigenvalue parameter dependent boundary conditions. We compare the 4-th order canonical forms to the canonical forms derived in this article.