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On Small Complete Sets of Functions
Published online by Cambridge University Press: 20 November 2018
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 ${{T}_{\alpha }}\,\subset \,{{\mathbf{C}}^{2}}$. The completeness theorem is a direct consequence of the Cauchy Residue Theorem in a torus. With suitable modifications the same result holds in ${{\mathbf{C}}^{n}}$.
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- Copyright © Canadian Mathematical Society 2000
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