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.
@article{TIMM_2005_11_2_a10,
author = {Yu. N. Subbotin and N. I. Chernykh},
title = {Construction of wavelets in $W_2^m(\mathbb R)$ and their approximative properties in different metrics},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {131--167},
publisher = {mathdoc},
volume = {11},
number = {2},
year = {2005},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2005_11_2_a10/}
}
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%0 Journal Article %A Yu. N. Subbotin %A N. I. Chernykh %T Construction of wavelets in $W_2^m(\mathbb R)$ and their approximative properties in different metrics %J Trudy Instituta matematiki i mehaniki %D 2005 %P 131-167 %V 11 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2005_11_2_a10/ %G ru %F TIMM_2005_11_2_a10
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/