周期Riemann边值问题

,,,,In this paper, theperiodic Riemann boundary value problems with the solutions allowed unbounded at $z=pminfty i$ is discussed. When the jump curve is a closed curve,by using the transformation $zeta= an{ rac {z} {a}}$, the singularities of the original problem at $z=pm infty{m i}$ become the poles at $zeta=pm ,i$, then removing the singularitythe periodic Riemann boundary value problem is transferred to the classical Riemann boundary value problem.,,When the jump curve is the real axis, by using the transformation $omega =e^{i z}$ the singularities of the solution for the periodic Riemann boundary value problem at $z=pminfty i$become the singularities for the poles at $omega=0$ and $omega=infty$, removing the singularity at $omega=0$, the periodic Riemann boundary value problem is also transferred into the Riemann boundary value Problem.