A necessary and sufficient condition is obtained for the generalized eigenfunction systems of 2 ×2 operator matrices to be a block Schauder basis of some Hilbert space, which offers a mathematical foundation of s...A necessary and sufficient condition is obtained for the generalized eigenfunction systems of 2 ×2 operator matrices to be a block Schauder basis of some Hilbert space, which offers a mathematical foundation of solving symplectic elasticity problems by using the method of separation of variables. Moreover, the theoretical result is applied to two plane elasticity problems via the separable Hamiltonian systems.展开更多
In this paper, we discuss some singulal integral operators, singular quadrature operators and discrethation matrices associated with singular integral equations of the first kind, and obtain some useful Properties for...In this paper, we discuss some singulal integral operators, singular quadrature operators and discrethation matrices associated with singular integral equations of the first kind, and obtain some useful Properties for them. Using these operators we give a unified framework for various collocation methods of numerical solutions of singular integral equations of the fine kind, which appears very simple.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 11361034 and 11371185)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20111501110001)the Natural Science Foundation of Inner Mongolia, China (Grant Nos. 2012MS0105 and 2013ZD01 )
文摘A necessary and sufficient condition is obtained for the generalized eigenfunction systems of 2 ×2 operator matrices to be a block Schauder basis of some Hilbert space, which offers a mathematical foundation of solving symplectic elasticity problems by using the method of separation of variables. Moreover, the theoretical result is applied to two plane elasticity problems via the separable Hamiltonian systems.
文摘In this paper, we discuss some singulal integral operators, singular quadrature operators and discrethation matrices associated with singular integral equations of the first kind, and obtain some useful Properties for them. Using these operators we give a unified framework for various collocation methods of numerical solutions of singular integral equations of the fine kind, which appears very simple.
