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Matematicheskie Zametki, 2001, Volume 69, Issue 5, Pages 699–707
DOI: https://doi.org/10.4213/mzm533 (Mi mzm533) 		 
This article is cited in 5 scientific papers (total in 5 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
Full-text PDF (205 kB) Citations (5)
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DOI: https://doi.org/10.4213/mzm533
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.
Received: 23.02.2000
English version:
Mathematical Notes, 2001, Volume 69, Issue 5, Pages 644–651
DOI: https://doi.org/10.1023/A:1010253609303
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
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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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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