On small complete sets of functions

Authors
Aizenberg, L Vidras, A
Citation
L. Aizenberg et A. Vidras, On small complete sets of functions, CAN J MATH, 52(1), 2000, pp. 3-30
Citations number
16
Categorie Soggetti
Mathematics
Journal title
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
ISSN journal
0008414X → ACNP
Volume
52
Issue
1
Year of publication
2000
Pages
3 - 30
Database
ISI
SICI code
0008-414X(200002)52:1<3:OSCSOF>2.0.ZU;2-E
Abstract
Using Local Residues and the Duality Principle a multidimensional variation of the completeness theorems by T. Carleman and A. F. Leontiev is proven f or the space of holomorphic functions defined on a suitable open strip T-al pha subset of C-2. The completeness theorem is a direct consequence of the Cauchy Residue Theorem in a torus. With suitable modifications the same res ult holds in C-n.