In this paper, a kind of new definitions of singular integral operators in the weighted L-2 space with the generalized Jacobi weights are given, then the boundedness in the weighted L-2 space, the relationships betwee...In this paper, a kind of new definitions of singular integral operators in the weighted L-2 space with the generalized Jacobi weights are given, then the boundedness in the weighted L-2 space, the relationships between these operators and the classic singular integral operators are proved. For the convenience in the later use, similar results in the L-2 space with Jacobi weights are given.展开更多
Abstract Asymptotic estimations of the Christoffel type functions for Lm extremal polynomials with an even integer m associated with generalized Jacobi weights are established. Also, asymptotic behavior of the zeros o...Abstract Asymptotic estimations of the Christoffel type functions for Lm extremal polynomials with an even integer m associated with generalized Jacobi weights are established. Also, asymptotic behavior of the zeros of the Lm extremal polynomials and the Cotes numbers of the corresponding Turán quadrature formula is given.展开更多
基金Supported by the Foundation of TY of China(10126028)
文摘In this paper, a kind of new definitions of singular integral operators in the weighted L-2 space with the generalized Jacobi weights are given, then the boundedness in the weighted L-2 space, the relationships between these operators and the classic singular integral operators are proved. For the convenience in the later use, similar results in the L-2 space with Jacobi weights are given.
基金Supported by the National Natural Science Foundation of China (No.19971089).
文摘Abstract Asymptotic estimations of the Christoffel type functions for Lm extremal polynomials with an even integer m associated with generalized Jacobi weights are established. Also, asymptotic behavior of the zeros of the Lm extremal polynomials and the Cotes numbers of the corresponding Turán quadrature formula is given.
