Computational Methods and Function Theory 8 (2008), No. 2, 625--640
Copyright Heldermann Verlag 2008
James E. Brennan
brennan@ms.uky.edu , University of Kentucky, Department of Mathematics, Lexington, KY 40506, U.S.A.
Let μ be a measure of compact support in the complex plane. In 1991 J. E. Thomson described completely the structure of Hp(μ), the closed subspace of Lp(μ) spanned by the polynomials, when 1≤ p<∞. Here we discuss the extent to which Rp(μ), the closed subspace of Lp(μ) spanned by the rational functions having no poles on the support of μ, admits a similar description.
Keywords: Rational approximation, analytic capacity, direct sum decomposition.
MSC 2000: Primary 30E10, 41A10, 41A20; Secondary 30C85, 30H05.
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