The Cousin and Poincare Problems

Authors : Cengiz ULUÇAY

Pages : 0-0

Doi:10.1501/Commua1_0000000098

View : 19 | Download : 7

Publication Date : 1981-01-01

Article Type : Research Paper

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 insert ignore into journalissuearticles values(connected öpen set);, and Ainsert ignore into journalissuearticles values(G); the ring insert ignore into journalissuearticles values(C- Algebra); of holomorphic functions on G. Then the set A of ali convergent power series insert ignore into journalissuearticles values(germs); representing the elements of Ainsert ignore into journalissuearticles values(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 : The Cousin, Poincare Problems, Mathematics