Geodesic
Universally optimal wavelets
Sbornik. Mathematics, Tome 188 (1997) no. 1, pp. 157-171

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A complete description of wavelet bases generated by a fixed function whose Fourier transform is the characteristic function of a set is presented. In particular, for the case of Sobolev spaces, wavelet bases are constructed possessing the following property of universal optimality: the subspaces generated by these functions are extremal for projection lattice widths (in the univariate case also for Kolmogorov widths) of the unit ball in $W^m_2(E_n)$ in the metric of $W^s_2(E_n)$ simultaneously for the whole scale of Sobolev classes (that is, for all $s,m\in E_1$, such that $s$). En route, certain results concerning completeness and the basis property of systems of exponentials are established. 
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     author = {N. A. Strelkov},
     title = {Universally optimal wavelets},
     journal = {Sbornik. Mathematics},
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     number = {1},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1997_188_1_a7/}
}
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N. A. Strelkov. Universally optimal wavelets. Sbornik. Mathematics, Tome 188 (1997) no. 1, pp. 157-171. http://geodesic.mathdoc.fr/item/SM_1997_188_1_a7/