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Mat. Sb., 2013, Volume 204, Number 6, Pages 135–160 (Mi msb7875)  

This article is cited in 3 scientific papers (total in 3 papers)

Littlewood polynomials and applications of them in the spectral theory of dynamical systems

A. A. Prikhod'ko

M. V. Lomonosov Moscow State University

Abstract: In this paper we establish the existence of character sums on the real line $\mathbb R$ that are $\varepsilon$-flat on any given compact subset $K\subset \mathbb R \setminus \{0\}$ with respect to the metric in the space $L^1(K)$. A consequence of this analytic result is an affirmative answer to Banach's conjecture on the existence of a dynamical system with a simple Lebesgue spectrum in the class of actions of the group $\mathbb R$.
Bibliography: 25 titles.

Keywords: Littlewood polynomials, van der Corput's method, Riesz products, rank-one flows, Banach's problem.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00759-а
Ministry of Education and Science of the Russian Federation НШ-3038.2008.1


DOI: https://doi.org/10.4213/sm7875

Full text: PDF file (808 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2013, 204:6, 910–935

Bibliographic databases:

UDC: 517.538
MSC: Primary 11L40, 37A10; Secondary 26D05, 28D05, 42A05
Received: 07.04.2011 and 01.04.2013

Citation: A. A. Prikhod'ko, “Littlewood polynomials and applications of them in the spectral theory of dynamical systems”, Mat. Sb., 204:6 (2013), 135–160; Sb. Math., 204:6 (2013), 910–935

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Ryzhikov, “Bounded ergodic constructions, disjointness, and weak limits of powers”, Trans. Moscow Math. Soc., 74 (2013), 165–171  mathnet  crossref  mathscinet  zmath  elib
    2. E. H. El Abdalaoui, “Generalized Riesz products on the Bohr compactification of ${\mathbb {R}}$”, J. Fourier Anal. Appl., 22:1 (2016), 20–35  crossref  mathscinet  zmath  isi  scopus
    3. A. A. Prikhod'ko, “On ergodic flows with simple Lebesgue spectrum”, Sb. Math., 211:4 (2020), 594–615  mathnet  crossref  crossref  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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