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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On approximation in the Bers spaces


Author: Charles K. Chui
Journal: Proc. Amer. Math. Soc. 40 (1973), 438-442
MSC: Primary 30A82
DOI: https://doi.org/10.1090/S0002-9939-1973-0340608-9
MathSciNet review: 0340608
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Abstract: Let $ D$ be a Jordan domain in the complex plane with rectifiable boundary $ C$. Let $ {A_q}(D)$ denote the Bers space with norm $ \vert\vert\;\vert{\vert _q}$. We prove that if $ f \in {A_q}(D),2 < q < \infty $, then there exist functions $ {s_n}(z) = \Sigma _{k = 1}^n1/(z - {z_{n,k}}),\;{z_{n,k}} \in C{\text{ for }}k = 1, \cdots ,n$, such that $ \vert\vert{s_n} - f\vert{\vert _q} \to 0$. This result does not hold for $ 1 < q \leqq 2$ even when $ D$ is a disc.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0340608-9
Keywords: Bers spaces, approximation, Jordan domain, gravitational field, unit masses
Article copyright: © Copyright 1973 American Mathematical Society