Approximation with scaled shift-invariant spaces by means of quasi-projection operators

Authors:
Rong-Qing Jia
Affiliations:
Department of Mathematics and Statistical Sciences, University of Alberta, Edmonton, Canada T6G 2G1
Venue:
Journal of Approximation Theory
Year:
2004

Citing 4
Cited 8

Using the refinement equations for the construction of Pre-Wavelets II: powers and two

Curves and surfaces
Approximation by multiinteger translates of functions having global support

Journal of Approximation Theory
Approximation from shift-invariant spaces by integral operators

SIAM Journal on Mathematical Analysis
Vector cascade algorithms and refinable function vectors in Sobolev spaces

Journal of Approximation Theory

Convergence rates of vector cascade algorithms in Lp

Journal of Approximation Theory
Quasi-interpolation in the Fourier algebra

Journal of Approximation Theory
Approximation by quasi-projection operators in Besov spaces

Journal of Approximation Theory
Convergence rates of vector cascade algorithms in Lp

Journal of Approximation Theory
C2 piecewise cubic quasi-interpolants on a 6-direction mesh

Journal of Approximation Theory
B-spline quasi-interpolation on sparse grids

Journal of Complexity
Full length article: On the density order of the principal shift-invariant subspaces of L2(Rd)

Journal of Approximation Theory
Full length article: Sampling approximation by framelets in Sobolev space and its application in modifying interpolating error

Journal of Approximation Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

The work of de Boor and Fix on spline approximation by quasiinterpolants has had far-reaching influence in approximation theory since publication of their paper in 1973. In this paper, we further develop their idea and investigate quasi-projection operators. We give sharp estimates in terms of moduli of smoothness for approximation with scaled shift-invariant spaces by means of quasi-projection operators. In particular, we provide error analysis for approximation of quasi-projection operators with Lipschitz spaces. The study of quasi-projection operators has many applications to various areas related to approximation theory and wavelet analysis.