Relationships among Three Multiplicities of a Differential Operator’s Eigenvalue

Shouzhong Fu, Zhong Wang

School of Mathematics and Statistics, Zhaoqing University, Guangdong, China.

DOI: 10.4236/am.2014.515211                

Abstract

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.

Keywords

Differential Operators, Eigenvalue, Algebraic Multiplicities, Geometric Multiplicities, Analytic Multiplicities

Conflicts of Interest

The authors declare no conflicts of interest.

References

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