An algebraic characterization of conformal equivalence of rectangular domains

Authors : İ. Kaya ÖZKIN

Pages : 0-0

Doi:10.1501/Commua1_0000000529

View : 6 | Download : 6

Publication Date : 1990-01-01

Article Type : Research Paper

Abstract :This paper presents a solution to a problem in the subject of rings of analytic functions. It was shown that [Bers insert ignore into journalissuearticles values(1948);, Kakutani insert ignore into journalissuearticles values(1955);] two domains Dj and D2 in the complex plane were conformally equivalent insert ignore into journalissuearticles values(to within a certain equivalence relation); iff the rings Binsert ignore into journalissuearticles values(DJ and Binsert ignore into journalissuearticles values(D2); of ali bounded analytic functions defined on them were algebraically isomorphic. In the case of rectangles, two are conformally equivalent iff the ration of the sides of one equals the same ratio for the other [Uluçay insert ignore into journalissuearticles values(1946);]. It follows that this ratio must be contained somewhere in the algebraic structure of the ring. The problem is to find it.
Keywords : algebraic, domains, equivalence