Mergelyan's Theorem is a result on the approximation of functions by polynomials in complex analysis, proved by the Armenian mathematician Sergei Mergelyan in 1951. It gives a sharp topological condition on a compact subset of the complex plane under which every function continuous on that set and holomorphic on its interior can be uniformly approximated as closely as desired by polynomials.
Facts
StatementFor a compact subset K of the complex plane whose complement is connected, every function continuous on K and holomorphic on the interior of K can be uniformly approximated on K by polynomials. 1 Classification
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Source Mergelyan's theorem (Wikipedia)
Principal Result Of
Source Sergey Mergelyan (Wikipedia)
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Source Mergelyan's theorem (Wikipedia)
Sources
1. Mergelyan's theorem (Wikipedia)
Lead section
Mergelyan's theorem is a result from approximation by polynomials in complex analysis proved by the Armenian mathematician Sergei Mergelyan in 1951.
Lead paragraph
Mergelyan's theorem is a result from approximation by polynomials in complex analysis proved by the Armenian mathematician Sergei Mergelyan in 1951.
Proved By: Sergey Mergelyan, Lead sentence
Mergelyan's theorem is a result from approximation by polynomials in complex analysis proved by the Armenian mathematician Sergei Mergelyan in 1951.
In Branch: Complex Analysis, Lead sentence
is a result from approximation by polynomials in complex analysis proved by the Armenian mathematician Sergei Mergelyan in 1951.
View the SourceSergey Mergelyan (Wikipedia)
Principal Result Of: Sergey Mergelyan, BiographyQuote, Principal Result Of: Sergey Mergelyan, Biography
In 1951 he formulated and proved the famous result from complex analysis called Mergelyan's theorem.
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