EN
The Cousin and Poincare Problems
Abstract
In this paper we feproduce the proofs of Cousin and Poincare problems for the structure sheaf A [5] without making explicit nse of flabby sheaf theory. We conciude with a Remark in section 3.
For the Solutions of these problems we shall merely make direct appeal to a property inherent to A, i.e., sections defined in A can be extended holomorphically to the entire region of definition.
We recall the foUotving Definitions. Let Gc: C", be a region (connected öpen set), and A(G) the ring (C- Algebra) of holomorphic functions on G. Then the set A of ali convergent power series (germs) representing the elements of A(G) is called a restricted sheaf över G.
It was proved in [1 ] that A is coherent as soon as G is a region of holomorphy.
Keywords
References
- Ankara Üniversitesi – Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Dergisi
Details
Primary Language
English
Subjects
Mathematical Sciences
Journal Section
Research Article
Authors
Cengiz Uluçay
This is me
Türkiye
Publication Date
January 1, 1981
Submission Date
January 1, 1981
Acceptance Date
-
Published in Issue
Year 1970 Volume: 30
APA
Uluçay, C. (1981). The Cousin and Poincare Problems. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 30. https://doi.org/10.1501/Commua1_0000000098
AMA
1.Uluçay C. The Cousin and Poincare Problems. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 1981;30. doi:10.1501/Commua1_0000000098
Chicago
Uluçay, Cengiz. 1981. “The Cousin and Poincare Problems”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 30 (January). https://doi.org/10.1501/Commua1_0000000098.
EndNote
Uluçay C (January 1, 1981) The Cousin and Poincare Problems. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 30
IEEE
[1]C. Uluçay, “The Cousin and Poincare Problems”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 30, Jan. 1981, doi: 10.1501/Commua1_0000000098.
ISNAD
Uluçay, Cengiz. “The Cousin and Poincare Problems”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 30 (January 1, 1981). https://doi.org/10.1501/Commua1_0000000098.
JAMA
1.Uluçay C. The Cousin and Poincare Problems. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 1981;30. doi:10.1501/Commua1_0000000098.
MLA
Uluçay, Cengiz. “The Cousin and Poincare Problems”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 30, Jan. 1981, doi:10.1501/Commua1_0000000098.
Vancouver
1.Cengiz Uluçay. The Cousin and Poincare Problems. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 1981 Jan. 1;30. doi:10.1501/Commua1_0000000098
