论文标题
Chui在伯格曼空间中的猜想
Chui's conjecture in Bergman spaces
论文作者
论文摘要
我们在加权（Hilbert）Bergman空间中最简单的分数（即带有单位系数的Cauchy核的总和）解决了Chui的猜想。也就是说，对于宽类的权重，我们证明，对于单位圆圈上$ n $杆的最简单分数在每$ n $中，并且只有当杆子在圆圈上均值时才时，则只有最小的规范。我们发现这些规范的尖锐渐近学。此外，我们使用$ l^2 $版本的汤普森定理（Thompson's Theorem）的$ l^2 $版本对最简单的近似值进行了$ l^2 $版本，以最简单的近似值来描述最简单的部分。
We solve Chui's conjecture on the simplest fractions (i.e., sums of Cauchy kernels with unit coefficients) in weighted (Hilbert) Bergman spaces. Namely, for a wide class of weights, we prove that for every $N$, the simplest fractions with $N$ poles on the unit circle have minimal norm if and only if the poles are equispaced on the circle. We find sharp asymptotics of these norms. Furthermore, we describe the closure of the simplest fractions in weighted Bergman spaces, using an $L^2$ version of Thompson's theorem on dominated approximation by simplest fractions.
