| 乔艳芬,侯国林,阿拉坦仓.一类4×4无界算子矩阵的本征向量组的块状基性质及其在弹性力学中的应用*[J].数学年刊A辑,2021,42(3):237~258 |
| 一类4×4无界算子矩阵的本征向量组的块状基性质及其在弹性力学中的应用* |
| Block Basis Property for Systems of Eigenvectors of a Class of 4×4 Unbounded Operator Matrices and Its Application in Elasticity |
| Received:March 23, 2020 Revised:March 05, 2021 |
| DOI：10.16205/j.cnki.cama.2021.0019 |
| 中文关键词: 本征向量组, Hamilton 算子, 本征值问题, 块状Schauder基, 矩形薄板 |
| 英文关键词:Eigenvector systems, Hamiltonian operator, Eigenvalue problem,Block Schauder basis, Rectangular thin plate |
| 基金项目:国家自然科学基金(No.11861048, No.11761029), 高等学校青年科技英才计划项目(No.NJYT-15-B03), 内蒙古自治区自然科学基金(No.2021MS01004)和内蒙古自治区研究生科研创新计划 (No.11200-12110201) |
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| 中文摘要: |
| 本文讨论了力学中出现的一类4×4无界Hamilton算子矩阵的本征向量组的块状Schauder基性质.在一定的条件下, 考虑了此类Hamilton算子矩阵的本征值问题, 进而给出了其本征向量组是某个Hilbert空间的一组块状Schauder基的一个充要条件,并通过矩形薄板的自由振动和弯曲问题验证了所得结果的有效性. |
| 英文摘要: |
| This paper deals with the block Schauder basis property of system of eigenvectors of a class of 4 × 4 unbounded Hamiltonian operator matrices appearing in mechanics.Under certain conditions, the eigenvalue problems of the Hamiltonian operator matrix are considered. Then a necessary and sufficient condition is presented for the system of eigenvectors of the Hamiltonian operator matrix to be a block Schauder basis of some Hilbert space. Moreover, the validity of the results is verified by the free vibration and bending problems of rectangular thin plates. |
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