Results 91 to 100 of about 1,731 (125)

Local Regularity of L∞ ∞-Refinable Function Vectors

Journal of Fourier Analysis and Applications, 2005
This article discusses the local regularity of refinable function vectors associated with a dilation matrix M. Suppose that D is a complete set of representatives of Zs/MZs. Under the assumptions that the self-affine tile T (M,D), associated with dilation matrix M and digit set D, has measure 1 and that the corresponding refinable function vector φ ∈ L∞
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A study of refinable function vectors via a nonlinear operator

Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96), 2002
This paper studies a certain nonlinear operator T from L/sup 2/(R,C/sup N/) to itself under which every refinable function vector is a fixed point. The iterations T/sup n/f of T on any f/spl isin/L/sup 2/(R,C/sup N/) with the Riesz basis property are investigated; they turn out to be the "cascade algorithm" iterates of f with weights depending on f ...
null Ying Huang, B. Suter
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Analysis of Refinable Vector Functions

2017
As we discussed in Chap. 4, framelets and wavelets are often derived from a refinable vector function \(\phi = (\phi _{1},\ldots,\phi _{r})^{\mathsf{T}}\) satisfying the following refinement equation.
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Construction of Smooth Refinable Function Vectors by Cascade Algorithms

SIAM Journal on Numerical Analysis, 2002
The refinement equation \(\Phi= \sum_{\alpha=0}^N a(\alpha)\Phi(2\cdot- \alpha)\), for \(r\)-dimensional vector function is considered. The sequence of \(r\times r\) matrices \(a=\{a(\alpha)\}_{\alpha=0,...,N}\) is called a refinement mask. The normalized solution of this equation is denoted by \(\Phi_a\). The cascade algorithm associated with the mask
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Generalized Refinable Function Vectors with Hermite Interpolating Property

Applied Mechanics and Materials, 2011
Wavelet analysis has many applications in scientific areas such as computer graphics, image processing, numerical algorithms and signal denoising. In general, a wavelet is derived from a refinable function vector via a multiresolution analysis. In this paper, we presented a novel notion of generalized Hermite interpolating refinable function vector. In
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Piecewise $\mathbf {H^1}$ functions and vector fields associated with meshes generated by independent refinements

Mathematics of Computation, 2014
Summary: We consider piecewise \( H^1\) functions and vector fields associated with a class of meshes generated by independent refinements and show that they can be effectively analyzed in terms of the number of refinement levels and the shape regularity of the subdomains that appear in the meshes.
Brenner, Susanne C., Sung, Li-Yeng
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Construction of a class of compactly supported symmetric and balanced refinable function vector by GTST

Applied Mathematics and Computation, 2009
The authors study the construction of balanced and symmetric refinable function vectors by general two-scale similarity transform (GTST). With GTST, the authors provide an algorithm to construct balanced refinable function vectors from unbalanced one. Furthermore, the algorithm also preserves the symmetry of refinable function vectors.
Yang, Shouzhi, Huang, Yongdong
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Hermite-Like Interpolating Refinable Function Vector and Its Application in Signal Recovering

Journal of Fourier Analysis and Applications, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Interpolating refinable function vectors and matrix extension with symmetry

2010
In Chapters 1 and 2, we introduce the definition of interpolating refinable function vectors in dimension one and high dimensions, characterize such interpolating refinable function vectors in terms of their masks, and derive their sum rule structure explicitly.
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Kronecker Type Convolution of Function Vectors with one Refinable Factor

2001
The aim of this paper is the further investigation of some of the properties being preserved when convolving two function vectors. This work follows the investigations in [6] of convolved refinable function vectors i.e.,function vectors which are solutions of matrix refinement equations.
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