论文信息 - On Small Complete Sets of Functions

On Small Complete Sets of Functions

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 ${{\mathbf{C}}^{n}}$ .

L. Aĭzenberg | A. Vidras

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