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# On Small Complete Sets of Functions

Published:2000-02-01
Printed: Feb 2000
• Lev Aizenberg
• Alekos Vidras
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## Abstract

Using Local Residues and the Duality Principle a multidimensional variation of the completeness theorems by T.~Carleman and A.~F.~Leontiev is proven for the space of holomorphic functions defined on a suitable open strip $T_{\alpha}\subset {\bf C}^2$. The completeness theorem is a direct consequence of the Cauchy Residue Theorem in a torus. With suitable modifications the same result holds in ${\bf C}^n$.
 MSC Classifications: 32A10 - Holomorphic functions 42C30 - Completeness of sets of functions