无穷维Hamilton算子辛自伴延拓的存在性与唯一性研究
Research on Existence and Uniqueness of Symplectic Self-Adjoint Extension of Infinite Dimensional Hamiltonian Operator
DOI: 10.12677/AAM.2019.86126, PDF,    国家自然科学基金支持
作者: 王 梅, 吴德玉：内蒙古大学数学科学学院，内蒙古 呼和浩特
关键词: 无穷维Hamilton算子；辛自伴延拓；Dimensional Hamiltonian Infinite Operator； Symplectic Self-Adjoint Extension
摘要: 本文研究了无穷维Hamilton算子的辛自伴延拓问题，利用空间分解的方法，给出了Hamilton算子存在辛自伴延拓的条件，还给出了辛自伴延拓唯一的条件。
Abstract: In this paper, the symplectic self-adjoint extension problem of infinite dimensional Hamiltonian operator is studied. By using the method of space decomposition, the condition of dimensional Hamiltonian Infinite operator exists symplectic self-adjoint extension is given, and the conditions of symplectic self-adjoint extension which is unique are given.
文章引用：王梅, 吴德玉. 无穷维Hamilton算子辛自伴延拓的存在性与唯一性研究[J]. 应用数学进展, 2019, 8(6): 1094-1100. https://doi.org/10.12677/AAM.2019.86126

参考文献

[1] 吴德玉, 阿拉坦仓. 分块算子矩阵谱理论及其应用[M]. 北京: 科学出版社, 2013.
[2] 钟万勰. 弹性力学求解新体系[M]. 大连: 大连理工大学出版社, 1995.
[3] Chen, A., Jin, G.H. and Wu, D.Y. (2015) On Symplectic Self-Adjointness of Hamiltonianperator Matrices. Science China, 58, 821-828. [Google Scholar] [CrossRef] 
[4] 刘景麟. 关于J对称算子的J自伴延拓[J]. 内蒙古大学学报(自然科学版), 1992, 23(3): 312-316.
[5] Reed, M. and Simon, B. (1978) Methods of Modern Mathematical Physics 1. Analysis of Operators. Academic Press, London.
[6] Weidmann, J. (1980) Linear Operators in Hilbert Spaces. Springer-Verlag, New York. [Google Scholar] [CrossRef] 

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