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Infinite systems of linear equations for real analytic functions


Authors: P. Domanski and D. Vogt
Journal: Proc. Amer. Math. Soc. 132 (2004), 3607-3614
MSC (2000): Primary 46E10; Secondary 46A13, 26E05, 46F15
Published electronically: July 20, 2004
MathSciNet review: 2084083
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Abstract | References | Similar Articles | Additional Information

Abstract: We study the problem when an infinite system of linear functional equations

\begin{displaymath}\mu_n(f)=b_n\quad\text{for }n\in\mathbb{N}\end{displaymath}

has a real analytic solution $f$ on $\omega\subseteq\mathbb{R} ^d$ for every right-hand side $(b_n)_{n\in\mathbb{N} }\subseteq\mathbb{C} $ and give a complete characterization of such sequences of analytic functionals $(\mu_n)$. We also show that every open set $\omega\subseteq\mathbb{R} ^d$ has a complex neighbourhood $\Omega\subseteq\mathbb{C} ^d$ such that the positive answer is equivalent to the positive answer for the analogous question with solutions holomorphic on $\Omega$.


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Additional Information

P. Domanski
Affiliation: Faculty of Mathematics and Computer Science, A. Mickiewicz University Poznań and Institute of Mathematics, Polish Academy of Sciences (Poznań branch), ul. Umultowska 87, 61-614 Poznań, Poland
Email: domanski@amu.edu.pl

D. Vogt
Affiliation: Bergische Universität Wuppertal, FB Mathematik, Gaußstr. 20, D–42097 Wuppertal, Germany
Email: dvogt@math.uni-wuppertal.de

DOI: https://doi.org/10.1090/S0002-9939-04-07435-0
Keywords: Space of real analytic functions, analytic functionals, interpolation of real analytic functions, Eidelheit sequence
Received by editor(s): January 28, 2003
Received by editor(s) in revised form: May 22, 2003, and July 9, 2003
Published electronically: July 20, 2004
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2004 American Mathematical Society