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Refinable Functions with PV Dilations [PDF]
, 2017 A PV number is an algebraic integer $\alpha$ of degree $d \geq 2$ all of whose Galois conjugates other than itself have modulus less than $1$. Erd\"{o}s \cite{erdos} proved that the Fourier transform $\widehat \varphi,$ of a nonzero compactly supported ...
Wayne Lawton
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Approximation by Multiple Refinable Functions [PDF]
Canadian Journal of Mathematics, 1997 AbstractWe consider the shift-invariant space, š(Ī¦), generated by a set Ī¦ = {Ī¦1,..., Ī¦r} of compactly supported distributions on R when the vector of distributions Ļ:= {Ī¦1,..., Ī¦r} 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.
Rong Qing Jia +2 more
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The Sobolev Regularity of Refinable Functions
Journal of Approximation Theory, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Amos Ron, Zuowei Shen
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The dynamics of COVID-19 in the UAE based on fractional derivative modeling using Riesz wavelets simulation [PDF]
Advances in Difference Equations, 2021 The well-known novel virus (COVID-19) is a new strain of coronavirus family, declared by the World Health Organization (WHO) as a dangerous epidemic. More than 3.5 million positive cases and 250 thousand deaths (up to May 5, 2020) caused by COVID-19 and ...
Mutaz Mohammad +2 more
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Approximation by crystal-refinable functions [PDF]
Geometriae Dedicata, 2019 Let $ $ be a crystal group in $\mathbb R^d$. A function $ :\mathbb R^d\longrightarrow \mathbb C$ is said to be {\em crystal-refinable} (or $ -$refinable) if it is a linear combination of finitely many of the rescaled and translated functions $ ( ^{-1}(ax))$, where the {\em translations} $ $ are taken on a crystal group $ $, and $a$ is an ...
U. Molter, M. Moure, Alejandro Quintero
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Quincunx Fundamental Refinable Functions in Arbitrary Dimensions
Axioms, 2017 In this paper, we generalize the family of DeslauriersāDubucās interpolatory masks from dimension one to arbitrary dimensions with respect to the quincunx dilation matrices, thereby providing a family of quincunx fundamental refinable functions in ...
Xiaosheng Zhuang
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An Efficient Method Based on Framelets for Solving Fractional Volterra Integral Equations [PDF]
Entropy, 2020 This paper is devoted to shedding some light on the advantages of using tight frame systems for solving some types of fractional Volterra integral equations (FVIEs) involved by the Caputo fractional order derivative.
Mutaz Mohammad +2 more
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Journal of Inequalities and Applications, 2016 In this paper, we construct a new family of refinable functions from generalized Bernstein polynomials, which include pseudo-splines of Type II. A comprehensive analysis of the refinable functions is carried out.
Ting Cheng, Xiaoyuan Yang
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Regularity of anisotropic refinable functions [PDF]
Applied and Computational Harmonic Analysis, 2017 This paper presents a detailed regularity analysis of anisotropic wavelet frames and subdivision. In the univariate setting, the smoothness of wavelet frames and subdivision is well understood by means of the matrix approach. In the multivariate setting, this approach has been extended only to the special case of isotropic refinement with the dilation ...
M. Charina, V. Protasov
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Refinable functions for dilation families [PDF]
Advances in Computational Mathematics, 2011 Advances in Computational Mathematics, 36 (3)
Philipp Grohs
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