论文标题
在$ \ ell^p_a $中的函数插值上
On Interpolation by Functions in $\ell^p_A$
论文作者
论文摘要
这项工作探讨了$ \ ell^p_a $的插值序列的几个方面，这是用$ p $ -summable Maclaurin系数在设备磁盘上的分析功能的空间。这项工作的大部分是通过Carlesonian镜头传达的。我们研究了格拉amian矩阵的各种类似物，为此，我们表明有界条件是必要的，足以插值，包括在Riesz系统方面对通用插值序列的表征。我们还讨论了弱分离，并使用伪血液指标的概括给出了此类序列的表征。最后，我们考虑Carleson的措施和嵌入。
This work explores several aspects of interpolating sequences for $\ell^p_A$, the space of analytic functions on the unit disk with $p$-summable Maclaurin coefficients. Much of this work is communicated through a Carlesonian lens. We investigate various analogues of Gramian matrices, for which we show boundedness conditions are necessary and sufficient for interpolation, including a characterization of universal interpolating sequences in terms of Riesz systems. We also discuss weak separation, giving a characterization of such sequences using a generalization of the pseudohyperbolic metric. Lastly, we consider Carleson measures and embeddings.
