Perturbing PLA

Gady Kozma; Alexander Olevskii

doi:10.1007/s11854-013-0036-8

Perturbing PLA

Gady Kozma
, Alexander Olevskii

Weizmann Institute of Science, Tel Aviv University

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

Abstract

We proved earlier that every measurable function on the circle, after a uniformly small perturbation, can be written as a power series (i.e., a series of exponentials with positive frequencies), which converges almost everywhere. Here, we show that this result is basically sharp: the perturbation cannot be made smooth or even Hölder. We also discuss a similar problem for perturbations with lacunary spectrum.

Original language	English GB
Pages (from-to)	279-298
Number of pages	20
Journal	Journal D Analyse Mathematique
Volume	121
Issue number	1
DOIs	https://doi.org/10.1007/s11854-013-0036-8
State	Published - Oct 2013

ASJC Scopus subject areas

Analysis
General Mathematics

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10.1007/s11854-013-0036-8

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title = "Perturbing PLA",

abstract = "We proved earlier that every measurable function on the circle, after a uniformly small perturbation, can be written as a power series (i.e., a series of exponentials with positive frequencies), which converges almost everywhere. Here, we show that this result is basically sharp: the perturbation cannot be made smooth or even H{\"o}lder. We also discuss a similar problem for perturbations with lacunary spectrum.",

author = "Gady Kozma and Alexander Olevskii",

note = "Israel Science FoundationBoth authors partially supported by their respective Israel Science Foundation grants.",

year = "2013",

month = oct,

doi = "10.1007/s11854-013-0036-8",

language = "الإنجليزيّة",

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AU - Kozma, Gady

AU - Olevskii, Alexander

N1 - Israel Science FoundationBoth authors partially supported by their respective Israel Science Foundation grants.

PY - 2013/10

Y1 - 2013/10

N2 - We proved earlier that every measurable function on the circle, after a uniformly small perturbation, can be written as a power series (i.e., a series of exponentials with positive frequencies), which converges almost everywhere. Here, we show that this result is basically sharp: the perturbation cannot be made smooth or even Hölder. We also discuss a similar problem for perturbations with lacunary spectrum.

AB - We proved earlier that every measurable function on the circle, after a uniformly small perturbation, can be written as a power series (i.e., a series of exponentials with positive frequencies), which converges almost everywhere. Here, we show that this result is basically sharp: the perturbation cannot be made smooth or even Hölder. We also discuss a similar problem for perturbations with lacunary spectrum.

UR - https://www.scopus.com/pages/publications/84888046826

U2 - 10.1007/s11854-013-0036-8

DO - 10.1007/s11854-013-0036-8

M3 - مقالة

SN - 0021-7670

VL - 121

SP - 279

EP - 298

JO - Journal D Analyse Mathematique

JF - Journal D Analyse Mathematique

IS - 1

ER -

Perturbing PLA

Abstract

ASJC Scopus subject areas

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