Geodesic
Construction of wavelets in $W_2^m(\mathbb R)$ and their approximative properties in different metrics
Trudy Instituta matematiki i mehaniki, Function theory, Tome 11 (2005) no. 2, pp. 131-167
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Wavelet bases in the Sobolev space $W_2^m(\mathbb R)$ on the axis $\mathbb R=(-\infty,\infty)$ orthogonal with respect to any given inner product generating one of equivalent norms in $W_2^m(\mathbb R)$ are constructed. The rate of convergence of series in these bases for smooth functions from $L_q(\mathbb R)$ ($2\le q\le\infty$) is investigated. 
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Yu. N. Subbotin; N. I. Chernykh. Construction of wavelets in $W_2^m(\mathbb R)$ and their approximative properties in different metrics. Trudy Instituta matematiki i mehaniki, Function theory, Tome 11 (2005) no. 2, pp. 131-167. http://geodesic.mathdoc.fr/item/TIMM_2005_11_2_a10/

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