About: Walsh–Lebesgue theorem

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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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  • 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. (en)
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  • 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. (en)
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  • Walsh–Lebesgue theorem (en)
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