Archiv der Mathematik

, Volume 87, Issue 6, pp 554–563 | Cite as

Periodic functions with bounded remainder

Article

Abstract.

Let F be the class of all 1-periodic real functions with absolutely convergent Fourier series expansion and let (xn)n ≧ 0 be the van der Corput sequence. In this paper results on the boundedness of
$$ \sum\limits_{n = 0}^{N - 1} {f(x_n )} for f \in F $$
are given. We give a criterion on the convergence rate of the Fourier coefficients of f such that the above sum is bounded independently of N. Further we show that our result is also best possible.

Mathematics Subject Classification (2000).

11K06 11K38 

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Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.School of MathematicsUniversity of New South WalesSydneyAustralia
  2. 2.Institut für FinanzmathematikUniversität LinzLinzAustria

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