Geodesic
On the Convergence of Orthorecursive Expansions in Nonorthogonal Wavelets
Matematičeskie zametki, Tome 92 (2012) no. 5, pp. 707-720

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The present paper is concerned with orthorecursive expansions which are generalizations of orthogonal series to families of nonorthogonal wavelets, binary contractions and integer shifts of a given function $\varphi$. It is established that, under certain not too rigid constraints on the function $\varphi$, the expansion for any function $f\in L^2(\mathbb{R})$ converges to $f$ in $L^2(\mathbb{R})$. Such an expansion method is stable with respect to errors in the calculation of the coefficients. The results admit a generalization to the $n$-dimensional case.
Keywords: orthorecursive expansion, Parseval's equality, Bessel's identity, trigonometric system, Jackson's inequality.
Mots-clés : nonorthogonal wavelets 
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     author = {A. Yu. Kudryavtsev},
     title = {On the {Convergence} of {Orthorecursive} {Expansions} in {Nonorthogonal} {Wavelets}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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     year = {2012},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_5_a6/}
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A. Yu. Kudryavtsev. On the Convergence of Orthorecursive Expansions in Nonorthogonal Wavelets. Matematičeskie zametki, Tome 92 (2012) no. 5, pp. 707-720. http://geodesic.mathdoc.fr/item/MZM_2012_92_5_a6/