Reproducing kernel of the space $R^t(K,\mu)$

Liming Yang

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arXiv · 1904.13311

Reproducing kernel of the space $R^t(K,\mu)$

Liming Yang

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Abstract

For $1 \le t < \infty ,$ a compact subset $K$ of the complex plane $\mathbb C,$ and a finite positive measure $\mu$ supported on $K,$ $R^t(K, \mu)$ denotes the closure in $L^t (\mu )$ of rational functions with poles off $K$. Let $\Omega$ be a connected component of the set of analytic bounded point evaluations for $R^t(K, \mu)$. In this paper, we examine the behavior of the reproducing kernel of $R^t(K, \mu)$ near the boundary $\partial \Omega \cap \mathbb T$, assuming that $\mu (\partial \Omega \cap \mathbb T ) > 0$, where $\mathbb T$ is the unit circle.

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BibTeX RIS

Liming Yang. 2019-04-30. Reproducing kernel of the space $R^t(K,\mu)$. https://arxiv.org/abs/1904.13311

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