Relationships among Three Multiplicities of a Differential Operator’s Eigenvalue

• 作者: Shouzhong Fu Zhong Wang
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Differential Operators EIGENVALUE ALGEBRAIC MULTIPLICITIES GEOMETRIC MULTIPLICITIES ANALYTIC MULTIPLICITIES
• 年，卷（期）: 2014,（15）
• 页码范围: 2185-2194
• 页数: 10页
• 分类号: O1

摘要

In this paper, the algebraic, geometric and analytic multiplicities of an eigenvalue for linear differential operators are defined and classified. The relationships among three multiplicities of an eigenvalue of the linear differential operator are given, and a fundamental fact that the algebraic, geometric and analytic multiplicities for any eigenvalue of self-adjoint differential operators are equal is proven.