Mathematical Notes

, Volume 69, Issue 5–6, pp 644–651 | Cite as

Comparison of the >L1-Norms of Total and Truncated Exponential Sums

  • S. V. Konyagin
  • M. A. Skopina


The paper is concerned with a conjecture stated by S. V. Bochkarev in the seventies. He assumed that there exists a “stability” for the L1-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 L1-norm of a sum of one-dimensional harmonics is replaced by the Lebesgue constant of a polyhedron of sufficiently high dimension.

Littlewood conjecture L1-norm of an exponential sum general orthonormal systems Lebesgue constant of a polyhedron 


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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • S. V. Konyagin
    • 1
  • M. A. Skopina
    • 2
  1. 1.M.~V.~Lomonosov Moscow State UniversityRussia
  2. 2.St. Petersburg State UniversityRussia

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