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Search: MSC category 42C30 ( Completeness of sets of functions )

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1. CJM 2000 (vol 52 pp. 3)

Aizenberg, Lev; Vidras, Alekos
On Small Complete Sets of Functions
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 ${\bf C}^n$.

Categories:32A10, 42C30

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