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This article is cited in 9 scientific papers (total in 9 papers)
On the Convergence of Orthorecursive Expansions in Nonorthogonal Wavelets
A. Yu. Kudryavtsev Moscow State Institute of International Relations (University) of the Ministry for Foreign Affairs of Russia
Abstract:
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, nonorthogonal wavelets, Parseval's equality, Bessel's identity, trigonometric system, Jackson's inequality.
Received: 14.09.2011
Citation:
A. Yu. Kudryavtsev, “On the Convergence of Orthorecursive Expansions in Nonorthogonal Wavelets”, Mat. Zametki, 92:5 (2012), 707–720; Math. Notes, 92:5 (2012), 643–656
Linking options:
https://www.mathnet.ru/eng/mzm8933https://doi.org/10.4213/mzm8933 https://www.mathnet.ru/eng/mzm/v92/i5/p707
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