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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
Article
  • 48 Downloads

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.

Keywords

Russia Fourier Continuous Function Abelian Group Fourier Series 
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References

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    S. V. Kislyakov, “A new correction theorem,” Izv. Akad. Nauk SSSR, Ser. Mat., 48, 305–330 (1984).zbMATHMathSciNetGoogle Scholar
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    S. V. Khrushchev, “Menshov’s correction theorem and Gaussian processes,” Trudy Mat. Inst. AN SSSR, 155, 151–181 (1981).zbMATHMathSciNetGoogle Scholar

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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