Abstract
Let E be a compact set in the plane, let LP(E) have its usual meaning, and let LP(E) be the subspace of functions analytic in the interior of E. The problem studied in this paper is whether or not rational functions with poles off E are dense in LP(E) (or in L"(E) in the case when E has no interior). For 1 ?p 2 which improve earlier results by Sinanjan. The results are given in terms of capacities.
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