Results 11 to 20 of about 2,702,060 (265)
The regularity of refinable functions [PDF]
Applied and Computational Harmonic Analysis, 2013 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 $C^\infty$.
Wang, Yang, Xu, Zhiqiang
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Orthogonality criteria for compactly supported refinable functions and refinable function vectors
The Journal of Fourier Analysis and Applications, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lagarias, Jeffrey C., Wang, Yang
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Approximation by crystal-refinable functions [PDF]
Geometriae Dedicata, 2019 Let $Γ$ be a crystal group in $\mathbb R^d$. A function $φ:\mathbb R^d\longrightarrow \mathbb C$ is said to be {\em crystal-refinable} (or $Γ-$refinable) if it is a linear combination of finitely many of the rescaled and translated functions $φ(γ^{-1}(ax))$, where the {\em translations} $γ$ are taken on a crystal group $Γ$, and $a$ is an expansive ...
Ursula Molter +2 more
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The limits of refinable functions [PDF]
Transactions of the American Mathematical Society, 2001 Summary: A function \(\phi\) is refinable (\(\phi \in S\)) if it is in the closed span of \(\{\phi(2x-k)\}\). This set \(S\) is not closed in \(L_{2}(\mathbb{R})\), and we characterize its closure. A necessary and sufficient condition for a function to be refinable is presented without any information on the refinement mask.
Strang, Gilbert, Zhou, Ding-Xuan
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Construction of Compactly Supported Refinable Componentwise Polynomial Functions in ℝ2 [PDF]
Abstract and Applied Analysis, 2011 We provide a sufficient condition for constructing a class of compactly supported refinable functions with componentwise polynomial property in ℝ2. An iteration algorithm is developed to compute the polynomial on each component of the functions' support.
Yanmei Xue, Ning Bi
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Multivariate Refinable Interpolating Functions [PDF]
Applied and Computational Harmonic Analysis, 1999 The author gives an algorithm for the construction of refinable interpolating functions for an arbitrary dilation matrix. This construction of refinable interpolating functions is an intermediate step in the construction of orthonormal wavelet bases and is of interest in its own right.
Derado, Josip
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Gauss Quadrature for Refinable Weight Functions [PDF]
Applied and Computational Harmonic Analysis, 2000 A refineable function \(\phi\) is a solution of a two-scale difference equation \[ \phi(x)= \sum_{j\in\mathbb{Z}} a_j\phi(2x- j), \] where \(a_j\) are real numbers satisfying \[ \sum_{j\in\mathbb{Z}} a_{k+ 2j}= 1,\quad\text{all }k\in\mathbb{Z}. \] The authors study Gaussian quadrature rules having refineable functions as weight functions.
Gautschi, Walter +2 more
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Refinable Functions with Compact Support [PDF]
Journal of Approximation Theory, 1996 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sun, Qiyu
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Applied General Topology, 2023 We introduce the notion of uniformly refinable map for compact, Hausdorff spaces, as a generalization of refinable maps originally defined for metric continua by Jo Ford (Heath) and Jack W. Rogers, Jr., Refinable maps, Colloq. Math., 39 (1978), 263-269.
Sergio Macías
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Fractal and Fractional, 2023 The Caputo fractional α-derivative ...
Gopalakrishnan Karnan, Chien-Chang Yen
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