On a filter for exponentially localized kernels based on Jacobi polynomials

DOI10.1016/j.jat.2009.01.004zbMath1203.42038OpenAlexW1965277554MaRDI QIDQ1041634

Jürgen Prestin, Hrushikesh N. Mhaskar, Frank-Dieter Filbir

Publication date: 3 December 2009

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2009.01.004

zbMATH Keywords

Riesz basisJacobi polynomialsspectral approximationslocalized filters and mollifiers

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Completeness of sets of functions in nontrigonometric harmonic analysis (42C30)

Related Items

Determination of jumps for functions via derivative Gabor series, Scattered data approximation on the bisphere and application to texture analysis, Localized Summability Kernels for Jacobi Expansions, Optimally space localized polynomials with applications in signal processing, Local approximation of operators, Applications of classical approximation theory to periodic basis function networks and computational harmonic analysis, A fully discretised filtered polynomial approximation on spherical shells, Filtered hyperinterpolation: a constructive polynomial approximation on the sphere, On Jacobi polynomials \(\mathscr{P}_k^{(\alpha,\beta)}\) and coefficients \(c_j^{\ell}(\alpha,\beta)\) \((k\geq 0, \ell =5,6; 1\leq j\leq \ell; \alpha,\beta > -1)\), On Jacobi polynomials and fractional spectral functions on compact symmetric spaces, Descriptions of fractional coefficients of Jacobi polynomial expansions

Uses Software

• OPQ

Cites Work

• Polynomial approximation of piecewise analytic functions
• Polynomial operators and local smoothness classes on the unit interval
• On local smoothness classes of periodic functions
• Sub-exponentially localized kernels and frames induced by orthogonal expansions
• Detection of edges from spectral data: new results
• Detection of edges in spectral data
• Orthogonal algebraic polynomial Schauder bases of optimal degree
• On the detection of singularities of a periodic function
• Diffusion polynomial frames on metric measure spaces
• Polynomial operators for spectral approximation of piecewise analytic functions
• A class of orthogonal polynomials
• Optimal filter and mollifier for piecewise smooth spectral data
• Convergence of Spectral Methods for Nonlinear Conservation Laws
• Approximation by Polynomials with Locally Geometric Rates
• Accurate Reconstructions of Functions of Finite Regularity from Truncated Fourier Series Expansions
• Polynomial approximation on the sphere using scattered data
• Jacobi Polynomials, II. An Analytic Proof of the Product Formula
• Adaptive filters for piecewise smooth spectral data*
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