- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 39
- An algebraic characterization of conformal equivalence of rectangular domains
An algebraic characterization of conformal equivalence of rectangular domains
Authors : I. Kaya Özkin
Pages : 0-0
Doi:10.1501/Commua1_0000000529
View : 6 | Download : 3
Publication Date : 1990-01-01
Article Type : Research
Abstract :This paper presents a solution to a problem in the subject of rings of analytic functions. It was shown that [Bers (1948), Kakutani (1955)] two domains Dj and D2 in the complex plane were conformally equivalent (to within a certain equivalence relation) iff the rings B(DJ and B(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 (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