Une version analytique du théorème de représentation de Menshov

Gady Kozma; Alexander Olevskiǐ

doi:10.1016/S0764-4442(00)01616-5

Une version analytique du théorème de représentation de Menshov

Translated title of the contribution: An "analytic" version of Menshov's representation theorem

Gady Kozma^*, Alexander Olevskiǐ

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

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

Translated title of the contribution	An "analytic" version of Menshov's representation theorem
Original language	French
Pages (from-to)	219-222
Number of pages	4
Journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	331
Issue number	3
DOIs	https://doi.org/10.1016/S0764-4442(00)01616-5
State	Published - 1 Aug 2000

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10.1016/S0764-4442(00)01616-5

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

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Une version analytique du théorème de représentation de Menshov

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