The point spectrum and non-degenerate symplectic structure of eigenfunction systems of off-diagonal infinite dimensional Hamiltonian operator H=(■)are studied in this article.The necessary and sufficient conditions f...The point spectrum and non-degenerate symplectic structure of eigenfunction systems of off-diagonal infinite dimensional Hamiltonian operator H=(■)are studied in this article.The necessary and sufficient conditions for the eigenfunction systems of off-diagonal infinite dimensional Hamiltonian operator H to have non-degenerate symplectic structure are given.Further,the necessary and sufficient conditions for point spectrum to be contained in real axis,imaginary axis and other areas are obtained for off-diagonal infinite dimensional Hamiltonian operator H,respectively.As an illustrating example,off-diagonal infinite dimensional Hamiltonian operators derived from the plate bending problem and string vibration problem are used to justify the conclusions.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11961022)the Natural Science Foundation of Inner Mongolia Autonomous Region(Grant Nos.2021MS01017,2021BS01007,2020ZD01)+3 种基金Inner Mongolia Higher Education Scientific Research Project(Grant Nos.NJZY21205,NJZY21208)University Basic Scientific Research Business Funding of Inner Mongolia(Grant No.ZSQN202216)Inner Mongolia“Grassland Talents”Industrial Innovation Talent Team ProjectResearch and Innovation Team Construction Plan of Hohhot Minzu College(Grant No.HM-TD-202005)。
文摘The point spectrum and non-degenerate symplectic structure of eigenfunction systems of off-diagonal infinite dimensional Hamiltonian operator H=(■)are studied in this article.The necessary and sufficient conditions for the eigenfunction systems of off-diagonal infinite dimensional Hamiltonian operator H to have non-degenerate symplectic structure are given.Further,the necessary and sufficient conditions for point spectrum to be contained in real axis,imaginary axis and other areas are obtained for off-diagonal infinite dimensional Hamiltonian operator H,respectively.As an illustrating example,off-diagonal infinite dimensional Hamiltonian operators derived from the plate bending problem and string vibration problem are used to justify the conclusions.
