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Statements

Subject Item: dbr:Joseph_L._Walsh
dbo:wikiPageWikiLink: dbr:Walsh–Lebesgue_theorem
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Subject Item: dbr:Walsh–Lebesgue_theorem
rdfs:label: Walsh–Lebesgue theorem
rdfs:comment: The Walsh–Lebesgue theorem is a famous result from harmonic analysis proved by the American mathematician Joseph L. Walsh in 1929, using results proved by Lebesgue in 1907. The theorem states the following: Let K be a compact subset of the Euclidean plane ℝ2 such the relative complement of with respect to ℝ2 is connected. Then, every real-valued continuous function on (i.e. the boundary of K) can be approximated uniformly on by (real-valued) harmonic polynomials in the real variables x and y.
dcterms:subject: dbc:Theorems_in_harmonic_analysis dbc:Theorems_in_approximation_theory
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dbo:abstract: The Walsh–Lebesgue theorem is a famous result from harmonic analysis proved by the American mathematician Joseph L. Walsh in 1929, using results proved by Lebesgue in 1907. The theorem states the following: Let K be a compact subset of the Euclidean plane ℝ2 such the relative complement of with respect to ℝ2 is connected. Then, every real-valued continuous function on (i.e. the boundary of K) can be approximated uniformly on by (real-valued) harmonic polynomials in the real variables x and y.
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Subject Item: dbr:Henri_Lebesgue
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Subject Item: dbr:List_of_things_named_after_Henri_Lebesgue
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Subject Item: wikipedia-en:Walsh–Lebesgue_theorem
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