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Probl. Anal. Issues Anal., 2017, Volume 6(24), Issue 1, Pages 11–18 (Mi pa213)  

Fourier coefficients of continuous functions with respect to localized Haar system

E. S. Belkinaa, Y. V. Malykhinb

a Petrozavodsk State University, 33, Lenina pr., Petrozavodsk, Russian Federation
b Steklov Mathematical Institute, 8, Gubkina st., Moscow, Russian Federation

Abstract: We construct a nontrivial example of a continuous function $f^*$ on $[0,1]^2$ which is orthogonal to tensor products of Haar functions supported on intervals of the same length. This example clarifies the possible behaviour of Fourier coefficients of continuous functions with respect to a localized Haar system. The function $f^*$ has fractal structure. We give lower bounds on its smoothness.

Keywords: fractals, Haar system, Haar wavelets.

DOI: https://doi.org/10.15393/j3.art.2017.3871

Full text: PDF file (566 kB)
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Bibliographic databases:

UDC: 517.518
MSC: 26B35, 42C10
Received: 15.04.2017
Revised: 15.06.2017
Accepted:19.06.2017
Language:

Citation: E. S. Belkina, Y. V. Malykhin, “Fourier coefficients of continuous functions with respect to localized Haar system”, Probl. Anal. Issues Anal., 6(24):1 (2017), 11–18

Citation in format AMSBIB
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\by E.~S.~Belkina, Y.~V.~Malykhin
\paper Fourier coefficients of continuous functions with respect to localized Haar system
\jour Probl. Anal. Issues Anal.
\yr 2017
\vol 6(24)
\issue 1
\pages 11--18
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