Approximation in the mean by rational functions |
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Authors: | James Zhijian Qiu |
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Institution: | (1) Department of Mathematics, Virginia Polytechnic Institute and State University, 24060 Blacksburg, VA |
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Abstract: | In this paper we proved that for a large class of compact subsetsK in the complex plane,R(K) is dense inL
q
() if and only if the set of analytic bounded point evaluations forR
q
(K, ) 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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Keywords: | Primary 47B20 Secondary 30H05 30E10 46E15 |
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