Approximation and Interpolation by Entire Functions of Several Variables

Canadian mathematical bulletin

关键词: entire function;    complex approximation;    interpolation;    several complex variables;   

DOI  :  10.4153/CMB-2010-006-4

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $fcolon mathbb R^no mathbb R$ be $C^infty$ and let $hcolonmathbb R^nomathbb R$ be positiveand continuous. For any unbounded nondecreasing sequence ${c_k}$of nonnegative real numbers and for any sequence withoutaccumulation points ${x_m}$ in $mathbb R^n$, there exists an entirefunction $gcolonmathbb C^nomathbb C$ taking real values on $mathbb R^n$ such thategin{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 thecase $n=1$ due to L. Hoischen.

【 授权许可】

Unknown