Approximation from Shift-Invariant Subspaces of L sup 2 (R sup d)

Abstract

A complete characterization is given of closed shift-invariant subspaces of which provide a specified approximation order. When such a space is principal (i.e., generated by a single function), then this characterization is in terms of the Fourier transform of the generator. As a special case, we obtain the classical Strang-Fix conditions, but without requiring the generating function to decay at infinity. The approximation order of a general closed shift-invariant space is shown to be already realized by a specifiable principal subspace.

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Document Details

Document Type
Technical Report
Publication Date
Jul 06, 1991
Accession Number
ADA238165

Entities

People

  • Amos Ron
  • Carl R. de Boor
  • Ronald A. Devore

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Analytic Functions
  • Equations
  • Exponential Functions
  • Finite Element Analysis
  • Fourier Analysis
  • Fourier Series
  • Functional Analysis
  • Inequalities
  • Interpolation
  • Linear Algebra
  • Literature
  • Military Research
  • New York
  • Periodic Functions
  • Polynomials
  • Sequences

Fields of Study

  • Mathematics

Readers

  • Battery Technology and Engineering
  • Calculus or Mathematical Analysis

Technology Areas

  • Space