Reproducing kernel of the space R^t(K,μ)

2019/04/30 by Yang, Liming
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1904.13311

Abstract

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

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