The characterization of the lune domains

Abstract

Let us consider a domain D that is bounded by two arcs of circles that intersect at points $alpha$ and $beta$ at angle $gamma=frac{pi}{m}$ This domain is called a lune. Let B(D) be an algebra of hounded analytic functions on D. In this paper taking complex algebra R, we give an algebric characterization of conformal mappings from D to U, by taking $alphavarepsilon R$ that satisfies certain conditions, where U = ${w varepsilon C:arrowvert warrowvert