Mathematical Notes

, Volume 69, Issue 3–4, pp 313–319

Extremum Problem for Periodic Functions Supported in a Ball

  • D. V. Gorbachev
Article

Abstract

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 problem periodic function Fourier coefficient asymptotic expansion entire function of exponential type 

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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

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

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