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.
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.
作者
乔艳芬
侯国林
阿拉坦仓
QIAO Yanfen;HOU Guolin;Alatancang(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China;Mathematics Science College,Inner Mongolia Normal University,Hohhot 010022,China)
出处
《数学年刊（A辑）》
CSCD
北大核心
2021年第3期237-258,共22页
Chinese Annals of Mathematics
基金
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)
内蒙古自治区研究生科研创新计划(No.11200-12110201)的资助.
