Classification of self-adjoint domains of odd-order differential operators with matrix theory

Abstract

In this article, we investigate the classification of self-adjoint boundary conditions of odd-order differential operators. We obtain that for odd-order self-adjoint boundary conditions under some assumptions, there are exactly two basic types of self-adjoint boundary conditions: coupled and mixed. Moreover we determine the number of possible conditions for each type, which is different from the even-order cases. Our construction will play an important role in the canonical forms and in the spectral analysis of these operators.

Keywords

• self-adjoint domains
• differential operators
• odd-order
• classification
• matrix theory
• 34l05
• 47e05