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arXiv math/05120032005-12-01math.CAmath.CV

An "Analytic" Version of Menshov's Representation Theorem

Gady Kozma, Alexander Olevskii

备注：: 4 pages. Announcement of math.CA/0510616. Should be identical to journal version except for the French abstract
发表信息：: C. R. Acad. Sci. Paris Ser. I Math. 331:3 (2000), 219--222
DOI：: 10.1016/S0764-4442(00)01616-5

英文摘要：

Every measurable function f on the circle can be represented as a sum of harmonics with positive spectrum, converging in measure. For convergence almost everywhere this is not true. We discuss several other subsets of Z for which one might get a Menshov type representation converging almost everywhere or in measure.

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