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On a theorem of
Mergelyan
John Brady Garnett |
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Vol. 26 (1968), No. 3, 461–467
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Abstract |
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The following is a theorem of S. N. Mergelyan. Theorem. If X is a compact plane set with finitely many complementary components, then every continuous function on X which is analytic on the interior is a uniform limit on X of rational functions. Here two short proofs of the theorem are given. Both proofs are obtained by considering the measures on X orthogonal to the algebra of rational functions. |
Mathematical Subject Classification
Primary: 46.55
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Milestones
Received: 25 May 1967
Published: 1 September 1968
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Authors |
| John Brady Garnett | |
| Department of Mathematics University of California Los Angeles CA 90024 United States |
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