Cantor uniqueness and multiplicity along subsequences

G. Kozma; A. Olevskiĭ; A. Olevski˘

doi:10.1090/spmj/1647

Cantor uniqueness and multiplicity along subsequences

G. Kozma, A. Olevskiĭ, A. Olevski˘

Weizmann Institute of Science, Tel Aviv University

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

Abstract

We construct a sequence c_{l}\to 0 such that the trigonometric series \sum c_{l}e^{ilx} converges to zero everywhere on a subsequence n_{k}. We show, for any such series, that the n_{k} must be very sparse, and that the support of the related distribution must be quite large.

Original language	English
Pages (from-to)	261-277
Number of pages	17
Journal	St. Petersburg Mathematical Journal
Volume	32
Issue number	2
DOIs	https://doi.org/10.1090/spmj/1647
State	Published - 1 Apr 2021

Keywords

Trigonometric series
localization principle
uniqueness

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Applied Mathematics

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10.1090/spmj/1647

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title = "Cantor uniqueness and multiplicity along subsequences",

abstract = "We construct a sequence c\_\{l\}\textbackslash{}to 0 such that the trigonometric series \textbackslash{}sum c\_\{l\}e\textasciicircum{}\{ilx\} converges to zero everywhere on a subsequence n\_\{k\}. We show, for any such series, that the n\_\{k\} must be very sparse, and that the support of the related distribution must be quite large.",

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AU - Olevskiĭ, A.

AU - Olevski˘, A.

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N2 - We construct a sequence c_{l}\to 0 such that the trigonometric series \sum c_{l}e^{ilx} converges to zero everywhere on a subsequence n_{k}. We show, for any such series, that the n_{k} must be very sparse, and that the support of the related distribution must be quite large.

AB - We construct a sequence c_{l}\to 0 such that the trigonometric series \sum c_{l}e^{ilx} converges to zero everywhere on a subsequence n_{k}. We show, for any such series, that the n_{k} must be very sparse, and that the support of the related distribution must be quite large.

KW - Trigonometric series

KW - localization principle

KW - uniqueness

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DO - 10.1090/spmj/1647

M3 - مقالة

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VL - 32

SP - 261

EP - 277

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

IS - 2

ER -

Cantor uniqueness and multiplicity along subsequences

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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