| On the Point Spectrum and Non-Degenerate Symplectic Structure of Eigenfunction Systems of Off-Diagonal Infinite Dimensional Hamiltonian Operators |
| Received:December 12, 2022 Revised:June 01, 2023 |
| Key Words:
point spectrum non-degenerate symplectic structure eigenfunction system off-diagonal infinite dimensional Hamiltonian operator
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| Fund Project: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), 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 Project, Research and Innovation Team Construction Plan of Hohhot Minzu College (Grant No.HM-TD-202005). |
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| Abstract: |
| The point spectrum and non-degenerate symplectic structure of eigenfunction systems of off-diagonal infinite dimensional Hamiltonian operator $H=\big(\begin{smallmatrix}0& B\\ C& 0\end{smallmatrix}\big)$ 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2023.06.007 |
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