Canonical forms for boundary conditions of self-adjoint differential operators

TL;DR

This paper extends the canonical forms for boundary conditions of self-adjoint differential operators to include 2n-th order cases, enhancing understanding of eigenvalues and aiding numerical computations.

Contribution

It derives new canonical forms for self-adjoint 2n-th order differential operators with eigenvalue-dependent boundary conditions, expanding beyond the previously known 4th order cases.

Findings

Derived canonical forms for 2n-th order operators.

Compared new forms with existing 4th order canonical forms.

Enhanced framework for eigenvalue analysis of higher-order 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.