Infinite systems of linear equations for real analytic functions期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Infinite systems of linear equations for real analytic functions

Authors:	P. Domanski D. Vogt

Affiliation:	Faculty of Mathematics and Computer Science, A. Mickiewicz University Poznan and Institute of Mathematics, Polish Academy of Sciences (Poznan branch), ul. Umultowska 87, 61-614 Poznan, Poland ; Bergische Universität Wuppertal, FB Mathematik, Gaußstr. 20, D--42097 Wuppertal, Germany

Abstract:	We study the problem when an infinite system of linear functional equations $begin{displaymath}mu_n(f)=b_nquadtext{for }ninmathbb{N}end{displaymath}$ has a real analytic solution on $omegasubseteqmathbb{R} ^d$ for every right-hand side $(b_n)_{ninmathbb{N} }subseteqmathbb{C}$ and give a complete characterization of such sequences of analytic functionals . We also show that every open set $omegasubseteqmathbb{R} ^d$ has a complex neighbourhood $Omegasubseteqmathbb{C} ^d$ such that the positive answer is equivalent to the positive answer for the analogous question with solutions holomorphic on .

Keywords:	Space of real analytic functions analytic functionals interpolation of real analytic functions Eidelheit sequence

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