Geodesic
Fourier coefficients of continuous functions with respect to localized Haar system
Problemy analiza, Tome 6 (2017) no. 1, pp. 11-18

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
E. S. Belkina; Y. V. Malykhin. Fourier coefficients of continuous functions with respect to localized Haar system. Problemy analiza, Tome 6 (2017) no. 1, pp. 11-18. http://geodesic.mathdoc.fr/item/PA_2017_6_1_a1/
@article{PA_2017_6_1_a1,
     author = {E. S. Belkina and Y. V. Malykhin},
     title = {Fourier coefficients of continuous functions with respect to localized {Haar} system},
     journal = {Problemy analiza},
     pages = {11--18},
     year = {2017},
     volume = {6},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2017_6_1_a1/}
}
TY  - JOUR
AU  - E. S. Belkina
AU  - Y. V. Malykhin
TI  - Fourier coefficients of continuous functions with respect to localized Haar system
JO  - Problemy analiza
PY  - 2017
SP  - 11
EP  - 18
VL  - 6
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/PA_2017_6_1_a1/
LA  - en
ID  - PA_2017_6_1_a1
ER  - 
%0 Journal Article
%A E. S. Belkina
%A Y. V. Malykhin
%T Fourier coefficients of continuous functions with respect to localized Haar system
%J Problemy analiza
%D 2017
%P 11-18
%V 6
%N 1
%U http://geodesic.mathdoc.fr/item/PA_2017_6_1_a1/
%G en
%F PA_2017_6_1_a1

[1] Kashin B. S., Sahakyan A. A., Orthogonal series, American Mathematical Soc., 2005, 451 pp. | MR

[2] Novikov I. Ya., Protasov V. Yu., Skopina M. A., Wavelet theory, American Mathematical Soc., 2011, 506 pp. | MR | Zbl