Approximation properties of multivariate wavelets

DOI10.1090/S0025-5718-98-00925-9zbMath0889.41013MaRDI QIDQ4383186

Rong-Qing Jia

Publication date: 24 March 1998

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

waveletsaccuracysmoothnessapproximation orderrefinable functionstransition operatorssubdivision operatorsrefinement equations

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Multidimensional problems (41A63) Rate of convergence, degree of approximation (41A25) Algorithms for approximation of functions (65D15)

Related Items

Highly symmetric \(\sqrt{3}\)-refinement bi-frames for surface multiresolution processing ⋮ Anisotropic bivariate subdivision with applications to multigrid ⋮ Density order of Parseval wavelet frames from extension principles ⋮ Characterization of Smoothness of Multivariate Refinable Functions in Sobolev Spaces ⋮ BIORTHOGONAL WAVELETS WITH SIX-FOLD AXIAL SYMMETRY FOR HEXAGONAL DATA AND TRIANGLE SURFACE MULTIRESOLUTION PROCESSING ⋮ Analytic functions in local shift-invariant spaces and analytic limits of level dependent subdivision ⋮ Convergence rates of cascade algorithms ⋮ WAVELETS WITH VANISHING MOMENTS ON THE HEISENBERG GROUP ⋮ Multivariate refinable Hermite interpolant ⋮ General solutions of matrix extension associated with multiple channel biorthogonal wavelet filters ⋮ Gibbs' phenomenon in higher dimensions ⋮ Non‐separable multivariate filter banks from univariate wavelets ⋮ Quasi-tight framelets with high vanishing moments derived from arbitrary refinable functions ⋮ Multiresolution expansion, approximation order and quasiasymptotic behavior of tempered distributions ⋮ Biorthogonal wavelets with 4-fold axial symmetry for quadrilateral surface multiresolution processing ⋮ Approximation properties of wavelets on p-adic fields ⋮ Rotation properties of 2D isotropic dilation matrices ⋮ Decompositions of trigonometric polynomials with applications to multivariate subdivision schemes ⋮ Reproducing solutions to PDEs by scaling functions ⋮ COMPACTLY SUPPORTED MULTIVARIATE, PAIRS OF DUAL WAVELET FRAMES OBTAINED BY CONVOLUTION ⋮ Highly symmetric bi-frames for triangle surface multiresolution processing ⋮ Multiple multivariate subdivision schemes: matrix and operator approaches ⋮ On the density order of the principal shift-invariant subspaces of \(L^2(\mathbb R^d)\) ⋮ Refinable functions with exponential decay: an approach via cascade algorithms ⋮ Symmetric orthogonal filters and wavelets with linear-phase moments ⋮ Subdivision schemes with general dilation in the geometric and nonlinear setting ⋮ Criteria for hierachical bases in Sobolev spaces ⋮ Bivariate two-band wavelets demystified ⋮ Convergence rate of vector subdivision scheme ⋮ Construction of symmetric or anti-symmetric B-spline wavelets and their dual wavelets ⋮ REFINABLE SHIFT INVARIANT SPACES IN ℝ^d ⋮ Characterization of Riesz bases of wavelets generated from multiresolution analysis ⋮ Regularity of non-stationary subdivision: a matrix approach ⋮ Construction of a class of multivariate compactly supported wavelet bases for \(L^2(\mathbb{R}^d)\) ⋮ Quincunx fundamental refinable functions and quincunx biorthogonal wavelets ⋮ Symmetry property and construction of wavelets with a general dilation matrix ⋮ Approximation orders of shift-invariant subspaces of \(W_{2}^{s}(\mathbb R^d)\) ⋮ Approximation properties and construction of Hermite interpolants and biorthogonal multiwavelets ⋮ On construction of multivariate wavelets with vanishing moments ⋮ Biorthogonal multivariate filter banks from centrally symmetric matrices ⋮ Accuracy conditions of multivariate refinable vector in frequency domain ⋮ Polynomial spaces reproduced by elliptic scaling functions ⋮ Bi-frames with 4-fold axial symmetry for quadrilateral surface multiresolution processing ⋮ Design of smooth orthogonal wavelets with beautiful structure from 2-band to 4-band ⋮ Lattice structure for paraunitary linear-phase filter banks with accuracy ⋮ Eigenvalues of scaling operators and a characterization of $B$-splines ⋮ Optimal $C^2$ two-dimensional interpolatory ternary subdivision schemes with two-ring stencils ⋮ Compactly supported tight wavelet frames and orthonormal wavelets of exponential decay with a general dilation matrix ⋮ Accuracy of lattice translates of several multidimensional refinable functions ⋮ SYMMETRIC MULTIVARIATE WAVELETS ⋮ Periodic interpolating-orthogonal bases of MRA and wavelets ⋮ Multivariate refinable interpolating functions ⋮ On construction of multivariate wavelet frames ⋮ A new subdivision method for bivariate splines on the four-directional mesh ⋮ The Sobolev regularity of refinable functions ⋮ Anisotropic dilations of shift-invariant subspaces and approximation properties in L2(Rd) ⋮ Accuracy of several multidimensional refinable distributions ⋮ Convergence of vector subdivision schemes in Sobolev spaces ⋮ Multivariate sampling-type approximation ⋮ Projectable multivariate refinable functions and biorthogonal wavelets. ⋮ Convergence of cascade algorithms in Sobolev spaces for perturbed refinement masks

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The polynomials in the linear span of integer translates of a compactly supported function
• Using the refinement equation for the construction of pre-wavelets. V: Extensibility of trigonometric polynomials
• Box splines
• A Bernstein-type inequality associated with wavelet decomposition
• A dual basis for the integer translates of an exponential box spline
• A sharp upper bound on the approximation order of smooth bivariate pp functions
• Approximation by translates of refinable functions
• A characterization of the approximation order for multivariate spline spaces
• Approximation Order from Bivariate C 1 -Cubics: A Counterexample
• Stationary subdivision
• Multiresolution analysis. Haar bases, and self-similar tilings of R/sup n/
• Two-Scale Difference Equations II. Local Regularity, Infinite Products of Matrices and Fractals
• Compression of Wavelet Decompositions
• Multivariate Refinement Equations and Convergence of Subdivision Schemes
• Approximation from Shift-Invariant Subspaces of L 2 (ℝ d )
• On linear independence for integer translates of a finite number of functions
• The Toeplitz Theorem and its Applications to Approximation Theory and Linear PDE's