无穷直线上N正则函数的Riemann边值问题

The Riemann Boundary Value Problem for N-Regular Functions on Infinite Straight Line

研究了N正则函数的零点和奇点的孤立性,并对它的孤立奇点进行了分类.给出了N正则函数在无穷直线上的Cauchy型积分,获得了该型积分边界值的P lem e lj公式.提出了N正则函数在无穷直线上的R iem ann边值问题R,讨论了该问题的特殊情形R0的可解性,并给出了该问题的非齐次情形的可解条件,获得了该问题的可解性定理.

The isolated properties of the zero and singular points for N-regular functions are investigated. The isolated singular points are classified. The Cauchy form integral and its boundary value formula of Plemelj for N-regular functions on infinite line are obtained. The Riemann boundary value problem for N-regular functions on infinite line are proposed. The solvability of the problem about its particular cases are discussed, an solvable condition of the problem for nonhomogeneous case is also obtained, the theorems of solvability of the problem are obtained.