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SINGULAR INTEGRAL OPERATORS IN L^2 SPACES ASSOCIATED WITH THE GENERALIZED JACOBI WEIGHTS
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作者 龚亚方 杜金元 《Acta Mathematica Scientia》 SCIE CSCD 2002年第4期484-488,共5页
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
关键词 singular integral operator generalized jacobi weight index
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ON THE ESTIMATION OF GENERALIZED LEBESGUE CONSTANT AND MODULUS OF GENERALIZED SINGULAR QUADRATURE FORMULAS AND ITS APPLICATION
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作者 蔡好涛 杜金元 《Acta Mathematica Scientia》 SCIE CSCD 2006年第4期610-614,共5页
This article, first gives the estimaties of two modulus, namely, generalized Lebesgue constant and modulus of generalized singular integral quadrature formulas, then applies them to obtain the error bounds of the oper... This article, first gives the estimaties of two modulus, namely, generalized Lebesgue constant and modulus of generalized singular integral quadrature formulas, then applies them to obtain the error bounds of the operator BL^Pm to the operator B. 展开更多
关键词 Cauchy kernel Dini conditions generalized jacobi weight
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Some Special Properties of Singular Integral Operators
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作者 Gong Ya-fang Du Jin-yuan 《Wuhan University Journal of Natural Sciences》 EI CAS 1999年第3期269-274,共6页
In this paper, we have proved some special properties of singular integral operators which are transformed from the singular integral equation defined in the interval (?1, 1), i.e., the properties of singular intergra... In this paper, we have proved some special properties of singular integral operators which are transformed from the singular integral equation defined in the interval (?1, 1), i.e., the properties of singular intergral operators at the endpoints and in the inner of (?1, 1). 展开更多
关键词 singular integral canonical function generalized jacobi weight
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Weighted Approximation by Multidimensional Baskakov Operators 被引量:1
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作者 游功强 宣培才 《Journal of Mathematical Research and Exposition》 CSCD 2000年第1期43-50,共8页
In this paper, we shall point out that the Multidimensional Baskakov opera- tors are unbounded in . Then we give a inverse theorems for multivariate Baskakov operators with Jacobi weights. A crucial tools in our app... In this paper, we shall point out that the Multidimensional Baskakov opera- tors are unbounded in . Then we give a inverse theorems for multivariate Baskakov operators with Jacobi weights. A crucial tools in our approach is a decompo- sition technique and a new type weights norm and flew K-function 展开更多
关键词 Multivariate Baskakov operators: jacobi weights weighted approximation claracterization.
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Orthogonal Polynomials with Respect to Modified JacobiWeight and Corresponding Quadrature Rules of Gaussian Type
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作者 Marija P.Stanic Aleksandar S.Cvetkovic 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2011年第4期478-488,共11页
In this paper we consider polynomials orthogonal with respect to the linear functional L:P→C,defined on the space of all algebraic polynomials P by L[p]=∫_(-1)^(1)p(x)(1−x)^(α−1/2)(1+x)^(β−1/2)exp(iζx)dx,whereα,... In this paper we consider polynomials orthogonal with respect to the linear functional L:P→C,defined on the space of all algebraic polynomials P by L[p]=∫_(-1)^(1)p(x)(1−x)^(α−1/2)(1+x)^(β−1/2)exp(iζx)dx,whereα,β>−1/2 are real numbers such thatℓ=|β−α|is a positive integer,andζ∈R\{0}.We prove the existence of such orthogonal polynomials for some pairs ofαandζand for all nonnegative integersℓ.For such orthogonal polynomials we derive three-term recurrence relations and also some differential-difference relations.For such orthogonal polynomials the corresponding quadrature rules of Gaussian type are considered.Also,some numerical examples are included. 展开更多
关键词 Orthogonal polynomials modified jacobi weight function recurrence relation Gaussian quadrature rule
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L_m Extremal Polynomials Associated with Generalized Jacobi Weights
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作者 Ying-guang ShiDepartment of Mathematics, Hunan Normal University, Changsha 410081, ChinaInstitute of Computational Mathematics&Scientific/Engineering Computing,Academy of Mathematics and System Science,Chinese Academy of Sciences,P.O.Box 2719,Beijing 100080,China 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2003年第2期205-218,共14页
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
关键词 Keywords L m extremal polynomials generalized jacobi weights Christoffel type functions
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SPECTRAL METHOD FOR MIXED INHOMOGENEOUS BOUNDARY VALUE PROBLEMS IN THREE DIMENSIONS 被引量:1
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作者 Tianjun Wang Benyu Guo Wei Li 《Journal of Computational Mathematics》 SCIE CSCD 2012年第6期579-600,共22页
In this paper, we investigate spectral method for mixed inhomogeneous boundary value problems in three dimensions. Some results on the three-dimensional Legendre approxima- tion in Jacobi weighted Sobolev space are es... In this paper, we investigate spectral method for mixed inhomogeneous boundary value problems in three dimensions. Some results on the three-dimensional Legendre approxima- tion in Jacobi weighted Sobolev space are established, which improve and generalize the existing results, and play an important role in numerical solutions of partial differential equations. We also develop a lifting technique, with which we could handle mixed inho- mogeneous boundary conditions easily. As examples of applications, spectral schemes are provided for three model problems with mixed inhomogeneous boundary conditions. The spectral accuracy in space of proposed algorithms is proved. Efficient implementations are presented. Numerical results demonstrate their high accuracy, and confirm the theoretical analysis well. 展开更多
关键词 Three-dimensional Legendre approximation in jacobi weighted Sobolev space Lifting technique Spectral method for mixed inhomogeneous boundary value problems.
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