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On Small Complete Sets of Functions

Published online by Cambridge University Press:  20 November 2018

Lev Aizenberg  and
Alekos Vidras
Lev Aizenberg
Affiliation:
Department of Mathematics and Computer Science, Bar-Ilan University, Ramat-Gan, Israel email: aizenbgr@macs.biu.ac.il
Alekos Vidras
Affiliation:
Department of Mathematics and Statistics, University of Cyprus, P.O.B 537, 1678 Nicosia, Cyprus email: msvidras@pythagoras.mas.ucy.ac.cy
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Abstract

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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 ${{T}_{\alpha }}\,\subset \,{{\mathbf{C}}^{2}}$. The completeness theorem is a direct consequence of the Cauchy Residue Theorem in a torus. With suitable modifications the same result holds in ${{\mathbf{C}}^{n}}$.

Keywords

32A1042C30
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 52 , Issue 1 , 01 February 2000 , pp. 3 - 30
Copyright
Copyright © Canadian Mathematical Society 2000

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