The Polynomials in the Linear Span of Integer Translates of a Compactly Supported Function.
Abstract
The linear span of integer translates of a fixed compactly supported function phi provides a particularly simple model of an approximating family of the finite element type. The approximating power of such a span (or, more precisely, of its scaled versions) has been known for some time to be characterizable in terms of the space pi phi of polynomials it contains. Recent work on box splines has provided concrete examples of interest in a multivariate settings and so rekindled interest in the space pi phi. The report derives and extends specific information about pi phi contained in recent work by Dahmen and Micchelli, and by Chui, Diamond, Jetter, Lai and Ward, but does so without reference to specific properties (such as piecewise polynomiality, or factorizablity of the Fourier transform) of phi. Understanding, in the simplest possible and most efficient terms, of the approximation power of such spaces may provide the necessary insight into approximation by smooth piecewise polynomials on regular, and perhaps even not so regular, partitions. Keywords: Quasi-interpolants; Invariance; and Box splines.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1986
- Accession Number
- ADA167530
Entities
People
- Carl R. de Boor
Organizations
- University of Wisconsin–Madison