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Orthogonality criteria for compactly supported refinable functions and refinable function vectors
Journal of Fourier Analysis and Applications, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lagarias, Jeffrey C., Wang, Yang
exaly +5 more sources
Refining perovskite structures to pair distribution function data using collective Glazer modes as a basis [PDF]
IUCrJ, 2022 Structural modelling of octahedral tilts in perovskites is typically carried out using the symmetry constraints of the resulting space group. In most cases, this introduces more degrees of freedom than those strictly necessary to describe only the ...
Sandra Helen Skjærvø +3 more
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On the power and promise of resonant diffraction for powders [PDF]
Structural DynamicsSignificantly more information is available if X-ray scattering and spectroscopic techniques are combined. In crystallography, structural information is encoded in the intensity of Bragg peaks, with the complex scattering power of each atom given by f(Q ...
Kevin H. Stone, Sikhumbuzo M. Masina
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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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The regularity of refinable functions
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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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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Refinable Functions with Compact Support
Journal of Approximation Theory, 1996 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sun, Qiyu
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Sobolev exponents of Butterworth refinable functions
Applied Mathematics Letters, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hong Oh Kim, Rae Young Kim
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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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Fractal and Fractional, 2023 The Caputo fractional α-derivative ...
Gopalakrishnan Karnan, Chien-Chang Yen
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