Représentation de fonctions non périodiques par des séries trigonométriques de fréquences presque entières

Gady Kozma; Alexander Olevskiǐ

doi:10.1016/S0764-4442(00)88566-3

Représentation de fonctions non périodiques par des séries trigonométriques de fréquences presque entières

Translated title of the contribution: Representation of non-periodic functions by trigonometric series with almost integer frequencies

Gady Kozma, Alexander Olevskiǐ

School of Mathematical Sciences

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

Abstract

Inspired by Men'shov's representation theorem, we prove that there exists a sequence {λ(n)} ⊂ ℝ̂, λ(n) = n + o(1), n ∈ ℤ, such that any measurable (complex valued) function f on ℝ can be represented as a sum of almost everywhere convergent trigonometric series (Equation presented).

Translated title of the contribution	Representation of non-periodic functions by trigonometric series with almost integer frequencies
Original language	French
Pages (from-to)	275-280
Number of pages	6
Journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	329
Issue number	4
DOIs	https://doi.org/10.1016/S0764-4442(00)88566-3
State	Published - Aug 1999

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abstract = "Inspired by Men'shov's representation theorem, we prove that there exists a sequence {λ(n)} ⊂ {\^ℝ}, λ(n) = n + o(1), n ∈ ℤ, such that any measurable (complex valued) function f on ℝ can be represented as a sum of almost everywhere convergent trigonometric series (Equation presented).",

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year = "1999",

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N2 - Inspired by Men'shov's representation theorem, we prove that there exists a sequence {λ(n)} ⊂ ℝ̂, λ(n) = n + o(1), n ∈ ℤ, such that any measurable (complex valued) function f on ℝ can be represented as a sum of almost everywhere convergent trigonometric series (Equation presented).

AB - Inspired by Men'shov's representation theorem, we prove that there exists a sequence {λ(n)} ⊂ ℝ̂, λ(n) = n + o(1), n ∈ ℤ, such that any measurable (complex valued) function f on ℝ can be represented as a sum of almost everywhere convergent trigonometric series (Equation presented).

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Représentation de fonctions non périodiques par des séries trigonométriques de fréquences presque entières

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