Rademacher–Menchov theorem

In mathematical analysis, the Rademacher–Menchov theorem, introduced by Rademacher (1922) and Menchoff (1923), gives a sufficient condition for a series of orthogonal functions on an interval to converge almost everywhere. == Statement == If the coefficients cν of a series of bounded orthogonal functions on an interval satisfy ∑ | c ν | 2 log ⁡ ( ν ) 2 < ∞ {\displaystyle \sum |c_{\nu }|^{2}\log(\nu )^{2}<\infty } then the series converges almost everywhere.

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Rademacher–Menchov theorem

In mathematical analysis, the Rademacher–Menchov theorem, introduced by Rademacher (1922) and Menchoff (1923), gives a sufficient condition for a series of orthogonal functions on an interval to converge almost everywhere. == Statement == If the coefficients cν of a series of bounded orthogonal functions on an interval satisfy ∑ | c ν | 2 log ⁡ ( ν ) 2 < ∞ {\displaystyle \sum |c_{\nu }|^{2}\log(\nu )^{2}<\infty } then the series converges almost everywhere.

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Source: Wikipedia "Rademacher–Menchov theorem" · CC BY-SA 4.0

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