Cauchy-Szegö 核的加权组合及其均值导数的最佳近似值

arXiv - MATH - Complex Variables Pub Date : 2024-09-17 DOI:arxiv-2409.10833

Viktor V. Savchuk, Maryna V. Savchuk

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引用次数: 0

摘要

在本文中，我们研究了一个关于单位盘$\mathbb D$上的哈代空间$H^1$内的最佳逼近的极值问题。具体地说，我们考虑了由内函数 $\varphi$ 和复数 $\lambda$ 为参数的 Cauchy-Szeg\"o 核及其导数的加权组合，并给出了子空间 $H^1_0$ 的最佳近似值 $e_\{varphi,z}(\lambda)$ 的明确公式。我们还描述了与该近似相关的极值函数。

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Best approximations for the weighted combination of the Cauchy--Szegö kernel and its derivative in the mean

In this paper, we study an extremal problem concerning best approximation in the Hardy space $H^1$ on the unit disk $\mathbb D$. Specifically, we consider weighted combinations of the Cauchy-Szeg\"o kernel and its derivative, parametrized by an inner function $\varphi$ and a complex number $\lambda$, and provide explicit formula of the best approximation $e_{\varphi,z}(\lambda)$ by the subspace $H^1_0$. We also describe the extremal functions associated with this approximation.

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arXiv - MATH - Complex Variables

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