Rademacher–Menchov theorem

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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[edit]

If the coefficients cν of a series of bounded orthogonal functions on an interval satisfy

\sum |c_\nu|^2\log(\nu)^2<\infty

then the series converges almost everywhere.

References[edit]