Geodesic
Fractal trigonometric approximation
Electronic transactions on numerical analysis, Tome 20 (2005), pp. 64-74
A general procedure to define nonsmooth fractal versions of classical trigonometric approximants is proposed. The systems of trigonometric polynomials in the space of continuous and periodic functions $\textcent $###$\sterling $########$\ddot $§$\copyright $are extended to bases of fractal analogues. As a consequence of the process, the density of trigonometric fractal functions in is deduced. We generalize also some classical results (Dini-Lipschitz's Theorem, for instance) $\textcent $###$\sterling $########$\ddot $§$\copyright $concerning the convergence of the Fourier series of a function of . Furthermore, a method for real data fitting $\textcent $###$\sterling $########$\ddot $§$\copyright $is proposed, by means of the construction of a fractal function proceeding from a classical approximant.
Classification : 37M10, 58C05
Keywords: iterated function systems, fractal interpolation functions, trigonometric approximation 
@article{ETNA_2005__20__a12,
     author = {Navascues,  M.A.},
     title = {Fractal trigonometric approximation},
     journal = {Electronic transactions on numerical analysis},
     pages = {64--74},
     year = {2005},
     volume = {20},
     zbl = {1091.42001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2005__20__a12/}
}
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UR  - http://geodesic.mathdoc.fr/item/ETNA_2005__20__a12/
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%0 Journal Article
%A Navascues,  M.A.
%T Fractal trigonometric approximation
%J Electronic transactions on numerical analysis
%D 2005
%P 64-74
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%U http://geodesic.mathdoc.fr/item/ETNA_2005__20__a12/
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%F ETNA_2005__20__a12
Navascues,  M.A. Fractal trigonometric approximation. Electronic transactions on numerical analysis, Tome 20 (2005), pp. 64-74. http://geodesic.mathdoc.fr/item/ETNA_2005__20__a12/