On Two Polynomial Spaces Associated with a Box Spline

Abstract

The polynomial space H in the span of the integer translates of a box spline M admits a well-known characterization as the joint kernel of a set of homogeneous differential operators with constant coefficients. The dual space H has a convenient representation by a polynomial space P, explicity known, which plays an important role in box spline theory as well as in multivariate polynomial interpolation. This paper characterized the dual space P as the joint kernel of simple differential operators, each one a power of a directional derivative. Various applications of this result to multivariate polynomial interpolation, multivariate splines and quality between polynomial and exponential spaces are discussed.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1989
Accession Number
ADA210559

Entities

People

  • Amos Ron
  • Carl R. de Boor
  • Nira Dyn

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Coefficients
  • Construction
  • Continents
  • Differential Equations
  • Directional
  • Equations
  • Exponential Functions
  • Generators
  • Geographic Regions
  • Inequalities
  • Interpolation
  • Linear Differential Equations
  • Linear Systems
  • North Carolina
  • Polynomials
  • United States
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Joint Military Operations and Doctrine.
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space