In this article, periodic Riemann boundary value problem with period 2aπ along closed smooth contours is discussed, and then singular integral equation with kernel csc t-t0/a along closed smooth contours restricted i...In this article, periodic Riemann boundary value problem with period 2aπ along closed smooth contours is discussed, and then singular integral equation with kernel csc t-t0/a along closed smooth contours restricted in the strip 0 〈 Rez 〈 aπ is discussed. Finally, the solutions with singularities of order one for the above two problems are discussed.展开更多
The basic sets of solutions in classH(orH *) for the characteristic equation and its adjoint equation with Hilbert kernel are given respectively. Thus the expressions of solutions and its solvable conditions are simpl...The basic sets of solutions in classH(orH *) for the characteristic equation and its adjoint equation with Hilbert kernel are given respectively. Thus the expressions of solutions and its solvable conditions are simplified. On this basis the solutions and the solvable conditions in classH 1 * as well as the generalized Noether theorem for the complete equation are obtained. Key words Hilbert kernel - solution with singularity of order one - basic set of solutions - Noether theorem - characteristic equation and its adjoint equation CLC number O 175.5 Foundation item: Supported by the National Natural Science Foundation of China (19971064) and Ziqiang Invention Foundation of Wuhan University (201990336)Biography: Zhong Shou-guo(1941-), male, Professor, research direction: singular integral equations and their applications.展开更多
After choosing weight functions suitably, we define a Banach spaceH ω μ (L) and discuss the generalized inverse of singular integral operators on an open arc. Using the generalized inverse, we obtain the solutions f...After choosing weight functions suitably, we define a Banach spaceH ω μ (L) and discuss the generalized inverse of singular integral operators on an open arc. Using the generalized inverse, we obtain the solutions for the following singular integral equation展开更多
In this paper, we study one kind of singular integral equations with singularity of order one. By the generalized Plemelj formula, this class of equations are transformed into a system of linear algebraic equations. I...In this paper, we study one kind of singular integral equations with singularity of order one. By the generalized Plemelj formula, this class of equations are transformed into a system of linear algebraic equations. In particular, we prove the existence of solution to the equation. The general solutions and the conditions of solvability are obtained in function class H.展开更多
基金Supported by the National Natural Science Foundation of China (19971064)
文摘In this article, periodic Riemann boundary value problem with period 2aπ along closed smooth contours is discussed, and then singular integral equation with kernel csc t-t0/a along closed smooth contours restricted in the strip 0 〈 Rez 〈 aπ is discussed. Finally, the solutions with singularities of order one for the above two problems are discussed.
文摘The basic sets of solutions in classH(orH *) for the characteristic equation and its adjoint equation with Hilbert kernel are given respectively. Thus the expressions of solutions and its solvable conditions are simplified. On this basis the solutions and the solvable conditions in classH 1 * as well as the generalized Noether theorem for the complete equation are obtained. Key words Hilbert kernel - solution with singularity of order one - basic set of solutions - Noether theorem - characteristic equation and its adjoint equation CLC number O 175.5 Foundation item: Supported by the National Natural Science Foundation of China (19971064) and Ziqiang Invention Foundation of Wuhan University (201990336)Biography: Zhong Shou-guo(1941-), male, Professor, research direction: singular integral equations and their applications.
基金Supported by the National Natural Science Foundation of China( No.2 0 1980 6 33)
文摘After choosing weight functions suitably, we define a Banach spaceH ω μ (L) and discuss the generalized inverse of singular integral operators on an open arc. Using the generalized inverse, we obtain the solutions for the following singular integral equation
基金Supported by the Qufu Normal University Youth Fund(XJ201218)
文摘In this paper, we study one kind of singular integral equations with singularity of order one. By the generalized Plemelj formula, this class of equations are transformed into a system of linear algebraic equations. In particular, we prove the existence of solution to the equation. The general solutions and the conditions of solvability are obtained in function class H.
