Periodic Riemann boundary value problem

Abstract

In this paper, we discuss the Riemann boundary value problems for the analytic functions with period in the situation where the solution can be unbounded at . When the jump curve is a closed contour, by using the tangent transformation , we transform the singularities on the z plane to the singularities on the ζ plane. When the jump curve is the real axis, by using the transformation , we transform the singularities on the z plane to the singularities 0 and ∞ on the ω plane. Thus, the original periodic Riemann boundary value problems are reduced to the classical Riemann boundary value problems whose solutions and the corresponding solvability conditions are well known.