Results 11 to 20 of about 10,821,939 (327)
The Regularity of Refinable Functions
Applied and Computational Harmonic Analysis, 2011 The regularity of refinable functions has been studied extensively in the past. A classical result by Daubechies and Lagarias states that a compactly supported refinable function in $\R$ of finite mask with integer dilation and translations cannot be in $C^\infty$.
Yang Wang, Zhiqiang Xu
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Regularity of Butterworth refinable functions [PDF]
Asian Journal of Mathematics, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aihua Fan, Qiyu Sun
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Nonlinear $N$-term approximation by refinable functions [PDF]
St. Petersburg Mathematical Journal, 2006 This interesting paper considers the \(N\)-term nonlinear approximation. This theory was essentially influenced by \textit{M. Sh. Birman} and \textit{M. Z. Solomjak} [Mat. Sb., N. Ser. 73(115), 331--355 (1967; Zbl 0173.16001)].
Yu. A. Brudnyi
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Refinable functions from Blaschke products
Rendiconti di Matematica e delle Sue Applicazioni, 2006 In this paper we study the problem of constructing refinable orthonormal cardinal functions from Blaschke products. The digital filter perspective of our construction corresponds to what is called an infinite impulse response (IIR) filter. We show how to construct, at least numerically, stable filters of this type in contrast to the Butterworth filter ...
Mariantonia Cotronei +4 more
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Neural Network Approximation of Refinable Functions [PDF]
IEEE Transactions on Information Theory, 2021 In the desire to quantify the success of neural networks in deep learning and other applications, there is a great interest in understanding which functions are efficiently approximated by the outputs of neural networks. By now, there exists a variety of
I. Daubechies +8 more
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Topological and geometric properties of refinable functions and MRA affine frames
, 2010 Deguang Han, Qiyu Sun, Wai-Shing Tang
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Unitary extension principle on zero-dimensional locally compact groups [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2023 In this article, we obtain methods for constructing step tight frames on an arbitrary locally compact zero-dimensional group. To do this, we use the principle of unitary extension.
Lukomskii, Sergei Feodorovich +1 more
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A new technique to estimate the regularity of refinable functions
, 1996 A. Clifford Cohen, Ingrid Daubechies
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Multivariate quasi-tight framelets with high balancing orders derived from any compactly supported refinable vector functions [PDF]
Science China Mathematics, 2020 Generalizing wavelets by adding desired redundancy and flexibility, framelets (i.e., wavelet frames) are of interest and importance in many applications such as image processing and numerical algorithms.
B. Han, Ran Lu
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On the Exact Evaluation of Integrals of Wavelets
Mathematics, 2023 Wavelet expansions are a powerful tool for constructing adaptive approximations. For this reason, they find applications in a variety of fields, from signal processing to approximation theory.
Enza Pellegrino +2 more
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