Journal of Mathematical Sciences

, Volume 172, Issue 2, pp 195–206 | Cite as

Correction up to a function with sparse spectrum and uniformly convergent Fourier series

  • P. IvanishviliEmail author
  • S. V. Kislyakov

In 1984, the second author proved that, after correction on a set of arbitrarily small measure, any continuous function on a finite-dimensional compact Abelian group acquires sparse spectrum and uniformly convergent Fourier series. In the present paper, we refine the result in two directions: first, we ensure uniform convergence in a stronger sense; second, we prove that the spectrum after correction can be put in even more peculiar sparse sets. Bibliography: 6 titles.


Russia Fourier Continuous Function Abelian Group Fourier Series 
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    F. G. Arutyunyan, “Representation of functions by multiple series,” Izv. Akad. Nauk Arm SSR, 64, 72–76 (1977).zbMATHGoogle Scholar
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Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.St.Petersburg State UniversitySt.PetersburgRussia
  2. 2.St.Petersburg Department of the Steklov Mathematical InstituteSt.PetersburgRussia

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