Mathematical Notes

, Volume 69, Issue 3, pp 313–319

Extremum Problem for Periodic Functions Supported in a Ball

  • D. V. Gorbachev

DOI: 10.1023/A:1010275206760

Cite this article as:
Gorbachev, D.V. Mathematical Notes (2001) 69: 313. doi:10.1023/A:1010275206760


We consider the Turan n-dimensional extremum problem of finding the value of An(hBn) which is equal to the maximum zero Fourier coefficient \(\widehat f_0\) of periodic functions f supported in the Euclidean ball hBn of radius h, having nonnegative Fourier coefficients, and satisfying the condition f(0)= 1. This problem originates from applications to number theory. The case of A1([−h,h]) was studied by S. B. Stechkin. For An(hBn we obtain an asymptotic series as h → 0 whose leading term is found by solving an n-dimensional extremum problem for entire functions of exponential type.

extremum problemperiodic functionFourier coefficientasymptotic expansionentire function of exponential type

Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • D. V. Gorbachev
    • 1
  1. 1.Tula State UniversityRussia