Abstract
In this paper we proved that for a large class of compact subsetsK in the complex plane,R(K) is dense inL q(μ) if and only if the set of analytic bounded point evaluations forR q(K, μ) is empty. As a consequence, we showed that this result is true for allK ifR(K) is replaced byA(K). Our main result includes the corresponding result of James Thomson for polynomials approximation as such a special case thatK is a disk.
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Qiu, J.Z. Approximation in the mean by rational functions. Integr equ oper theory 25, 235–252 (1996). https://doi.org/10.1007/BF01308633
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DOI: https://doi.org/10.1007/BF01308633