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An algebraic characterization of conformal equivalence of rectangular domains

Year 1990, Volume: 39 , - , 01.01.1990

İ. Kaya Özkın

https://doi.org/10.1501/Commua1_0000000529

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

References

  • Communications, Series A1:Mathematics and Statistics

Year 1990, Volume: 39 , - , 01.01.1990

İ. Kaya Özkın

https://doi.org/10.1501/Commua1_0000000529

Abstract

References

  • Communications, Series A1:Mathematics and Statistics
There are 1 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

İ. Kaya Özkın This is me

Publication Date January 1, 1990
Submission Date January 1, 1990
Published in Issue Year 1990 Volume: 39

Cite

APA Özkın, İ. K. (1990). An algebraic characterization of conformal equivalence of rectangular domains. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 39. https://doi.org/10.1501/Commua1_0000000529
AMA Özkın İK. An algebraic characterization of conformal equivalence of rectangular domains. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. January 1990;39. doi:10.1501/Commua1_0000000529
Chicago Özkın, İ. Kaya. “An Algebraic Characterization of Conformal Equivalence of Rectangular Domains”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 39, January (January 1990). https://doi.org/10.1501/Commua1_0000000529.
EndNote Özkın İK (January 1, 1990) An algebraic characterization of conformal equivalence of rectangular domains. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 39
IEEE İ. K. Özkın, “An algebraic characterization of conformal equivalence of rectangular domains”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 39, 1990, doi: 10.1501/Commua1_0000000529.
ISNAD Özkın, İ. Kaya. “An Algebraic Characterization of Conformal Equivalence of Rectangular Domains”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 39 (January 1990). https://doi.org/10.1501/Commua1_0000000529.
JAMA Özkın İK. An algebraic characterization of conformal equivalence of rectangular domains. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 1990;39. doi:10.1501/Commua1_0000000529.
MLA Özkın, İ. Kaya. “An Algebraic Characterization of Conformal Equivalence of Rectangular Domains”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 39, 1990, doi:10.1501/Commua1_0000000529.
Vancouver Özkın İK. An algebraic characterization of conformal equivalence of rectangular domains. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 1990;39.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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