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On Small Complete Sets of Functions

Open Access article
 Printed: Feb 2000
  • Lev Aizenberg
  • Alekos Vidras
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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, 42C30 show english descriptions Holomorphic functions
Completeness of sets of functions
32A10 - Holomorphic functions
42C30 - Completeness of sets of functions

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