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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
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
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
Linking options:
https://www.mathnet.ru/eng/mzm533https://doi.org/10.4213/mzm533 https://www.mathnet.ru/eng/mzm/v69/i5/p699
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Abstract page: | 653 | Full-text PDF : | 246 | References: | 83 | First page: | 4 |
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