The couple grade of Self-adjoint Domains of Singular Differential Operators

Jiong Sun; Wanyi Wang; Zhiming Zheng

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The couple grade of Self-adjoint Domains of Singular Differential Operators

Jiong Sun 1 *,Wanyi Wang 2,Zhiming Zheng 3

1.Department of Mathematics,Inner Mongolia University

2.（1) Department of Mathematics, Inner Mongolia University,（2）Department of Mathematics, Inner Mongolia Normal University

3.Department of Mathematics, Beihang University

*Correspondence author

#Submitted by

Subject:

Funding: 国家自然科学基金,国家自然科学基金,教育部博士点基金（No.10561005,10661008,20040126008 ）

Opened online:21 December 2007

Accepted by: none

Citation: Jiong Sun ,Wanyi Wang,Zhiming Zheng.The couple grade of Self-adjoint Domains of Singular Differential Operators[OL]. [21 December 2007] http://en.paper.edu.cn/en_releasepaper/content/17241

The self-adjoint domains associated with a scalar differential expression of an arbitrary even order are investigated in this paper. There is a known one-to-one correspondence between these domains and the complete Lagrangian subspaces of a naturally defined symplectic space. Using this correspondence, a characterization of the self-adjoint domains is obtained for the situations where the differential expression is regular at one of the end points of its interval and in either the limit-point category or the limit-circle category at the other end point. Moreover we get a complete describing on the couple-grade of boundary conditions, and point out there are how many classifications on the couple-grade of boundary conditions in limit-point and limit-circle cases.

Keywords:differential operator, couple-grade, boundary condition, self-adjoint, symplectic geometry,

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