An "Analytic" Version of Menshov's Representation Theorem

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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.
4 pages. Announcement of math.CA/0510616. Should be identical to journal version except for the French abstract

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Classical Analysis and ODEs, Complex Variables

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http://salesiana.dossiersoluciones.com/handle/123456789/106038

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0512003
 http://arxiv.org/abs/math/0512003
 C. R. Acad. Sci. Paris Ser. I Math. 331:3 (2000), 219--222
 doi:10.1016/S0764-4442(00)01616-5

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arXiv