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Generalized Pseudo-Butterworth Refinable Functions
Journal of Fourier Analysis and Applications, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Luo, Zhongxuan +3 more
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On the Regularity of Matrix Refinable Functions
SIAM Journal on Mathematical Analysis, 1998The refinable functions of this paper are vector functions \(\Phi\), that are solutions of a refinement equation of the form \(\Phi=\sum_\alpha P_\alpha \Phi(2\cdot-\alpha)\) where the sequence \(\{P_\alpha\}\) of \(r\times r\) matrices, or equivalently, the matrix function \(P(\omega)=2^{-d}\sum_\alpha P_\alpha e^{-i\alpha \omega}\) is called the ...
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Multivariate symmetric refinable functions and function vectors
International Journal of Wavelets, Multiresolution and Information Processing, 2016For any symmetry group [Formula: see text], any appropriate matrix dilation (compatible with [Formula: see text]) and any appropriate symmetry center [Formula: see text] we give an explicit method for the construction of [Formula: see text]-symmetric with respect to the center [Formula: see text] refinable masks which have sum rule of an arbitrary ...
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Causality properties of refinable functions and sequences
Advances in Computational Mathematics, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Goh, S.S., Goodman, T.N.T., Lee, S.L.
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Orthogonal polynomials and Gaussian quadrature for refinable weight functions [PDF]
Applied and Computational Harmonic Analysis, 2004 We show how to compute the modified moments of a refinable weight function directly from its mask in O(N2n) rational operations, where N is the desired number of moments and n the length of the mask. Three immediate applications of such moments are: •the
de Villiers, J.M., Laurie, D.P.
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Stability and Orthonormality of Multivariate Refinable Functions
SIAM Journal on Mathematical Analysis, 1997Summary: This paper characterizes the stability and orthonormality of the shifts of a multidimensional \((M,c)\) refinable function \(\phi\) in terms of the eigenvalues and eigenvectors of the transition operator \(W_{c_{\text{au}}}\) defined by the autocorrelation \(c_{\text{au}}\) of its refinement mask \(c, \) where \(M\) is an arbitrary dilation ...
Lawton, W., Lee, S.L., Shen, Z.
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Smoothness of refinable function vectors on ℝn
International Journal of Wavelets, Multiresolution and Information Processing, 2017Let [Formula: see text] be a dilation matrix, an [Formula: see text] expansive matrix that maps [Formula: see text] into itself. Let [Formula: see text] be a finite subset of [Formula: see text] and for [Formula: see text] let [Formula: see text] be [Formula: see text] complex matrices.
Ramazan Tinaztepe +2 more
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On refinable functions and subdivision with positive masks
Advances in Computational Mathematics, 2006The author considers univariate refinable functions with finite, positive mask. First he derives, explicitly in terms of the mask, estimates for the geometric convergence rate of both the cascade algorithm and the corresponding subdivision scheme, as well as the Hölder continuity exponent of the refinable function.
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Functions and Procedures in Refinement
1997The rules for introducing procedures and procedure calls will be illustrated using some familiar examples.
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A Class of Orthogonal Refinable Functions and Wavelets
Constructive Approximation, 2003A triple of continuous orthogonal refinable spline functions \((\varphi_1, \varphi_2, \varphi_3)\) with compact supports is constructed. For any \(n\geq 2\) they can have degree \(n - 1\) and simple knots in \({1\over 4}{\mathbb Z}\). The construction works for any multiresolution analysis \(\left(V_j\right)\), where \(V_0\) is generated by a single ...
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