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Mat. Zametki, 2001, Volume 69, Issue 5, Pages 699–707 (Mi mz533)  

This article is cited in 2 scientific papers (total in 2 papers)

Comparison of the $L^1$-Norms of Total and Truncated Exponential Sums

S. V. Konyagina, M. A. Skopinab

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Saint-Petersburg State University

Abstract: The paper is concerned with a conjecture stated by S. V. Bochkarev in the seventies. He assumed that there exists a stability for the $L^1$-norm of trigonometric polynomials when adding new harmonics. In particular, the validity of this conjecture implies the well-known Littlewood inequality. The disproof of a statement close to Bochkarev's conjecture is given. For this, the following method is used: the $L^1$-norm of a sum of one-dimensional harmonics is replaced by the Lebesgue constant of a polyhedron of sufficiently high dimension.

DOI: https://doi.org/10.4213/mzm533

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English version:
Mathematical Notes, 2001, 69:5, 644–651

Bibliographic databases:

Document Type: Article
UDC: 517.5
Received: 23.02.2000

Citation: S. V. Konyagin, M. A. Skopina, “Comparison of the $L^1$-Norms of Total and Truncated Exponential Sums”, Mat. Zametki, 69:5 (2001), 699–707; Math. Notes, 69:5 (2001), 644–651

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Konyagin S.V., Temlyakov V.N., “Convergence of greedy approximation I. General systems”, Studia Math., 159:1 (2003), 143–160  crossref  mathscinet  zmath  isi  scopus  scopus
    2. Üreten O., Tascioǧlu S., “Autocorrelation properties of OFDM timing synchronization waveforms employing pilot subcarriers”, EURASIP Journal on Wireless Communications and Networking, 2009, Special issue on synchronization in wireless communications, Article No.: 10  isi
  • Математические заметки Mathematical Notes
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