带Hilbert核的奇异积分方程及与其相关联的一些正交三角多项式组

带Hilbert核的奇异积分方程及与其相关联的一些正交三角多项式组 SOME SYSTEMS OF ORTHOGONAL TRIGONOMETRIC POLYNOMIALS ASSOCIATED WITH SINGULAR INTEGRAL EQUATIONS WITH HILBERT KERNEL 杜金元 Du Jinyuan 1 first-author Department of Mathematics Wuhan University Wuhan Hubei Department of Mathematics Wuhan University Wuhan Hubei Department of Mathematics, Wuhan University Department of Mathematics, Wuhan University 本文给出了带Hilbert核的奇异积分方程的标准化方程,归一化算子,约束算子;并且导出了与其相关联的两种权函数及两类正交三角多项式组;详细讨论了这些正交三角多项式的性质。这些,不仅改善了带Hilbert核的奇异积分方程的经典理论,而且将为其数值解法提供理论基础。 In this paper, some systems of orthogonal trigonometric polynomials as-sociated with singular integral equations with Hilbert kernel are derived, and some properties of these trigonometric polynomials are established. Moreover, we have introduced the normalized equation, the unisolved operator and the restricted operator of the singular integral equation with Hilbert kernel These results are both the improvements of the classical theory and the foundations of the method of numerical solutions, for singular integral equations with Hilbert kernel 奇异积分方程 标准化方程 归一化算子 约束算子 相关联的正交三角多项式组 singular integral equation Normalized equation Unisolved operator Restricted operator Systems of orthogonal triogonometric polynomials. 中国科学院科学基金 1988-02-01 2021-04-01 2