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Liouville, J. and Sturm, J.C.F. (1837) Extrait d’une méemoire sur le développement des fonctions en serie. Journal de Mathématiques Pures et Appliquées, 2, 220-223.

has been cited by the following article:

• TITLE: Relationships among Three Multiplicities of a Differential Operator’s Eigenvalue

  AUTHORS: Shouzhong Fu, Zhong Wang

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

  JOURNAL NAME: Applied Mathematics, Vol.5 No.15, August 5, 2014

  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.