Menshov representation spectra

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dc.creatorKozma, Gady
dc.creatorOlevskii, Alexander
dc.date2005-10-28
dc.date.accessioned2026-07-07T06:48:02Z
dc.date.available2026-07-07T06:48:02Z
dc.descriptionA Menshov spectrum is a subset of the integers that is sufficient for representing every measurable function as an almost-everywhere converging trigonometric (non-Fourier) sum. In this language the celebrated "Menshov representation theorem" states that Z is a Menshov spectrum. In this paper we construct 1) Menshov spectra that are almost exponentially sparse 2) that are almost squares. Then we show that the positive integers are not a Menshov spectrum but are a Menshov spectrum in measure, and repeat 1) and 2) in the analytic settings.
dc.description25 pages. Part of GK's PhD thesis
dc.identifierhttps://arxiv.org/abs/math/0510616
dc.identifierhttp://arxiv.org/abs/math/0510616
dc.identifierJ. Anal. Math. 84 (2001), 361-393
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/103853
dc.subjectClassical Analysis and ODEs
dc.subjectComplex Variables
dc.subject42b20
dc.titleMenshov representation spectra
dc.typetext

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