CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

Approximation and Interpolation by Entire Functions of Several Variables

  Published:2009-12-04
 Printed: Mar 2010
  • Maxim R. Burke
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   HTML   LaTeX   MathJax  

Abstract

Let $f\colon \mathbb R^n\to \mathbb R$ be $C^\infty$ and let $h\colon \mathbb R^n\to\mathbb R$ be positive and continuous. For any unbounded nondecreasing sequence $\{c_k\}$ of nonnegative real numbers and for any sequence without accumulation points $\{x_m\}$ in $\mathbb R^n$, there exists an entire function $g\colon\mathbb C^n\to\mathbb C$ taking real values on $\mathbb R^n$ such that \begin{align*} &|g^{(\alpha)}(x)-f^{(\alpha)}(x)|\lt h(x), \quad |x|\ge c_k, |\alpha|\le k, k=0,1,2,\dots, \\ &g^{(\alpha)}(x_m)=f^{(\alpha)}(x_m), \quad |x_m|\ge c_k, |\alpha|\le k, m,k=0,1,2,\dots. \end{align*} This is a version for functions of several variables of the case $n=1$ due to L. Hoischen.
Keywords: entire function, complex approximation, interpolation, several complex variables entire function, complex approximation, interpolation, several complex variables
MSC Classifications: 32A15 show english descriptions Entire functions 32A15 - Entire functions
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/