Approximation and commutator properties of projections onto shift-invariant subspaces and applications to boundary integral equations

DOI10.1216/jiea/1181074247zbMath0921.41004OpenAlexW2013935810MaRDI QIDQ1286347

Siegfried Prössdorf, Jörg Schult

Publication date: 3 May 1999

Published in: Journal of Integral Equations and Applications (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/jie/VOL10-4/CONT10-4/CONT10-4.html

zbMATH Keywords

periodic pseudodifferential equationsGalerkin-Petrov methods

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Numerical methods for integral equations (65R20) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Stability theory for integral equations (45M10) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Interpolation in approximation theory (41A05) Spline approximation (41A15) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Fredholm integral equations (45B05) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (3)

Qualocation for boundary integral equations using splines with multiple knots ⋮ Superapproximation for projections on spline spaces ⋮ Discrete orthogonal projections on multiple knot periodic splines

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The convergence of Galerkin and collocation methods with splines for pseudodifferential equations on closed curves
• Lokale Theorie des Reduktionsverfahrens für singuläre Integralgleichungen
• A spline collocation method for singular integral equations with piecewise continuous coefficients
• The convergence of spline collocation for strongly elliptic equations on curves
• A spline collocation method for multidimensional strongly elliptic pseudodifferential operators of order zero
• Numerical analysis for integral and related operator equations.
• Multilevel preconditioning
• Spline approximation methods for multidimensional periodic pseudodifferential equations
• Spline collocation for strongly elliptic equations on the torus
• Commutator properties for periodic splines
• Multiwavelet approximation methods for pseudodifferential equations on curves. Stability and convergence analysis
• Wavelet approximation methods for pseudodifferential equations. I: Stability and convergence
• The structure of finitely generated shift-invariant spaces in \(L_ 2(\mathbb{R}^ d)\)
• Approximation by multiinteger translates of functions having global support
• Wavelet approximation methods for pseudodifferential equations. II: Matrix compression and fast solution
• Boundary element collocation methods using splines with multiple knots
• On the linear independence of integer translates of box splines with rational directions
• On the Asymptotic Convergence of Collocation Methods
• A Finite Element Collocation Method for Singular Integral Equations
• Ein Lokalisierungsprinzip in der Theorie der Spline-Approximationen und einige Anwendungen
• Interpolation of Besov Spaces
• Lokale Theorie des Reduktionsverfahrens für Toeplitzoperatoren
• Stationary subdivision
• Approximation from Shift-Invariant Subspaces of L 2 (ℝ d )
• On Local Approximation Properties of L₂-Projection on Spline-Subspaces†
• On the Integer Translates of a Compactly Supported Function: Dual Bases and Linear Projectors

This page was built for publication: Approximation and commutator properties of projections onto shift-invariant subspaces and applications to boundary integral equations