The Szegö kernel and oblique projections: conformal mapping of non-smooth regions

The method of Kerzman and Trummer (J. Comp. Appl. Math. 14, 111–123, 1986) for computing the Riemann mapping function of a smooth domain is extended to include the case of simply connected convex regions with corners, in particular convex polygons. The connection between the Szegö kernel and the Riemann mapping function is classical. The integral equation in Kerzman and Trummer (J. Comp. Appl. Math. 14, 111–123, 1986) that determines the Szegö kernel is no longer defined in the presence of corners. We modify the equation by using new oblique projections. This approach is equivalent to employing preliminary mappings.