Results 221 to 230 of about 728 (254)
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A criterion for orthogonality of refinable functions
Applied Mathematics-A Journal of Chinese Universities, 2001This paper gives, a characterization for the orthonormality of matrix polynomials in refinable equations in multi-scale analysis.
Bi, Ning, Huang, Daren
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Computers and Mathematics With Applications, 2008 An algorithm for constructing a pair of biorthogonal two-direction refinable function and the corresponding biorthogonal two-direction wavelet is presented.
Xie, Changzhen
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Refinable Functions: Positivity and Interpolation
Analysis and Applications, 2003This paper examines two properties of refinable functions. The first provides conditions under which a refinable function is strictly positive and the other presents a conjecture about cardinal interpolation by refinable functions. The conjecture is supported by some analysis and also computation.
Micchelli, Charles A., Zhou, Ding-Xuan
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Regularity of Multivariate Refinable Functions
Constructive Approximation, 1999The regularity of univariate compactly supported refinable functions is known to be related to the spectral properties of an associated transfer operator. The authors derive similar results for the case of multivariate refinable functions with a general dilation matrix \(A\).
Cohen, A. +2 more
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Capabilities, Functionings and Refined Functionings
Journal of Human Development, 2006Sen's theory of capabilities is often presented as more comprehensive than an approach in terms of achievements (functionings) because it takes account of freedom and it contains at least as much information. This paper questions the last argument and argues that both kinds of consideration (freedom, comprehensive information) justify an approach in ...
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Approximation by Multiple Refinable Functions
Canadian Journal of Mathematics, 1997AbstractWe consider the shift-invariant space, 𝕊(Φ), generated by a set Φ = {Φ1,..., Φr} of compactly supported distributions on R when the vector of distributions ϕ:= {Φ1,..., Φr} T satisfies a system of refinement equations expressed in matrix form aswhere a is a finitely supported sequence of r x r matrices of complex numbers.
Jia, R. Q. +2 more
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A decay theorem for refinable functions
Applied Mathematics Letters, 1994 We show that a refinable function with absolutely summable mask cannot have exponential decay in both time and ...
Íngrid Daubechies
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Orthogonal polynomials and Gaussian quadrature for refinable weight functions
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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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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