奇异线性哈密顿算子自伴扩张的新描述
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摘要
研究了具有一个奇异端点的线性哈密顿算子的白伴扩张的解析描述.设最小哈密顿算子h的亏指数为(d,d),将Im(h~*y,y)表示为秩为2d的二次型,该文利用二次型的表示矩阵得到了最小哈密顿算子h的自伴扩张域的一种新的完全描述.
In this paper,the self-adjoint extension of the minimal Hamiltonian operator h with equal deficiency index(d,d) is considered.Since Im(h~*y,y) can be represented as a quadratic form with rank being 2d,the new characterization of the domains of self-adjoint extensions of h is obtained by the representation matrix.
In this paper,the self-adjoint extension of the minimal Hamiltonian operator h with equal deficiency index(d,d) is considered.Since Im(h~*y,y) can be represented as a quadratic form with rank being 2d,the new characterization of the domains of self-adjoint extensions of h is obtained by the representation matrix.
引文
[1]Everitt W N.Integrable-square solution of ordinary differential equations(III).Quart J Math,1963,14(2):170-180
[2]Everitt W N,Zettl A.Generalized symmetric ordinary differential expressions I:the general theory.Nieuw Archief voor Wiskunde,1979,27(3):363-397
[3]Cao Zhijiang.On self-adjoint domains of 2nd order differential operators in limit-cirle case.Acta Math Sinica,New Series,1985,1(3):175-180
[4]Krall A M.Hilbert Spaces,Boundary Value Problems and Orthogonal Polynomials.Basel,Boston,Berlin:Birkhauser-Verlag,2002
[5]Naimark M A.Linear Differential Operators.New York:Ungar,1968
[6]Shi Yuming.On the rank of the matrix radius of the limiting set for a singular linear Hamiltonian system.Linear ALgebra and its Applications,2004,376:109-123
[7]Sun Jiong,Wang Aiping,Anton Zettl.Continuous spectrum and square-integrable solutions of differential operators with intermediate deficiency index.Journal of Functional Analysis,2008,255:3229-3248
[8]Sun Jiong.On the self-adjoint extensions of symmetric ordinary differential operators with middle deficiency indices.Acta Math Sinica,New Series,1986,2(2):152-167
[9]Sun Huaqing,Shi Yuming.Self-adjoint extensions for singular linear Hamiltonian systems.Math Nachr,2011,284(5-6):797-814
[10]Weidmann J.Linear Operators in Hilbert Spaces.Berlin,New York:Springer-Verlag,1980
[11]Zheng Zhaowen,Chen Shaozhu.GKN theory for linear Hamiltonian systems.Applied Mathematics and Computation,2006,182:1514-1527
[12]曹之江.常微分算子.上海:上海科学技术出版社,1986
[13]曹之江.高阶极限圆型微分算子的自伴扩张.数学学报,1985,28(2):205-217
[14]魏广生.对称算子自伴域的一种新描述.内蒙古大学学报,1996,27(3):305-130
[15]魏广生,徐宗本.亏指数为可效无穷的对称微分算子的自伴扩张.数学进展,2000,29(3):227-234
[2]Everitt W N,Zettl A.Generalized symmetric ordinary differential expressions I:the general theory.Nieuw Archief voor Wiskunde,1979,27(3):363-397
[3]Cao Zhijiang.On self-adjoint domains of 2nd order differential operators in limit-cirle case.Acta Math Sinica,New Series,1985,1(3):175-180
[4]Krall A M.Hilbert Spaces,Boundary Value Problems and Orthogonal Polynomials.Basel,Boston,Berlin:Birkhauser-Verlag,2002
[5]Naimark M A.Linear Differential Operators.New York:Ungar,1968
[6]Shi Yuming.On the rank of the matrix radius of the limiting set for a singular linear Hamiltonian system.Linear ALgebra and its Applications,2004,376:109-123
[7]Sun Jiong,Wang Aiping,Anton Zettl.Continuous spectrum and square-integrable solutions of differential operators with intermediate deficiency index.Journal of Functional Analysis,2008,255:3229-3248
[8]Sun Jiong.On the self-adjoint extensions of symmetric ordinary differential operators with middle deficiency indices.Acta Math Sinica,New Series,1986,2(2):152-167
[9]Sun Huaqing,Shi Yuming.Self-adjoint extensions for singular linear Hamiltonian systems.Math Nachr,2011,284(5-6):797-814
[10]Weidmann J.Linear Operators in Hilbert Spaces.Berlin,New York:Springer-Verlag,1980
[11]Zheng Zhaowen,Chen Shaozhu.GKN theory for linear Hamiltonian systems.Applied Mathematics and Computation,2006,182:1514-1527
[12]曹之江.常微分算子.上海:上海科学技术出版社,1986
[13]曹之江.高阶极限圆型微分算子的自伴扩张.数学学报,1985,28(2):205-217
[14]魏广生.对称算子自伴域的一种新描述.内蒙古大学学报,1996,27(3):305-130
[15]魏广生,徐宗本.亏指数为可效无穷的对称微分算子的自伴扩张.数学进展,2000,29(3):227-234