The partial sum process of orthogonal expansion as geometric rough process with Fourier series as an example---an improvement of Menshov-Rademacher theorem

Details The partial sum process of orthogonal expansion as geometric rough process with Fourier series as an example---an improvement of Menshov-Rademacher theorem The partial sum process of orthogonal expansion as geometric rough process with Fourier series as an example---an improvement of Menshov-Rademacher theorem

2011-09-06

arxiv.org/abs/1109.1072v1

Mathematics

Classical Analysis and ODEs

Scientific paper

In this paper, we prove that the partial sum process of general orthogonal
series is a geometric 2-rough process under the same condition as in
Menshov-Rademacher Theorem. For Fourier series, the condition can be improved,
and an equivalent condition on the limit function is identified.

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