非正则函数组Riemann-Hilbert边值问题

讨论了一般情况下,非正则型函数组Riemann-Hilbert边值问题的求解。对原问题通过引入与正则型问题相同的变换,将问题化成为分别求解相对独立的一个Riemann边值问题和一个Hilbert边值问题;通过引入对角矩阵的方法,将非正则型问题化为正则型,求得一般解;对如何应用Hermite插值多项式的特点、将一般解简化为更为适用的形式作了说明。

Riemann - Hilbert Boundary Value Problem of Non - regular Equations

The solvation of Riemann-Hilbert boundary value of non-regular equations is discussed in generalized situation.By introducing a transform which has the same regular Riemann-Hilbert boundary value problems,the problems are separated into a Riemann boundary problm and Hilbert boundary problem which are solved individually.Then,some special diagonal matrices are introduced for helping to transfer those equations of Riemann-Hilbert boundary value problem to regular form and obtain the generalized solvation.Some illustration of the expression of the generalized solution is simplified by Hermite interpolation polynomials is given,in which,the form of solution can be reduced to a rather simper form.