论文标题
几个变量中的最佳近似值和正交多项式II：单位球中的多项式族
Optimal approximants and orthogonal polynomials in several variables II: families of polynomials in the unit ball
论文作者
论文摘要
我们获得了与功能$ f（z）= 1- \ frac {1} {\ sqrt {2}}（z_1+z_2）$以及单位$ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2- kernel $ $ $ 2- kernel $ ung $ lang lang lang（z_1+z_2）$（z_1+z_2）$相关的加权正交多项式和最佳近似值的封闭表达式。 z，w \ rangle）^{ - γ} $，$γ> 0 $。我们的论点是基本的，但不依赖于一维情况。
We obtain closed expressions for weighted orthogonal polynomials and optimal approximants associated with the function $f(z)=1-\frac{1}{\sqrt{2}}(z_1+z_2)$ and a scale of Hilbert function spaces in the unit $2$-ball having reproducing kernel $(1-\langle z,w\rangle)^{-γ}$, $γ>0$. Our arguments are elementary but do not rely on reduction to the one-dimensional case.
