Accession Number:

ADA210559

Title:

On Two Polynomial Spaces Associated with a Box Spline

Descriptive Note:

Technical summary rept.

Corporate Author:

WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES

Personal Author(s):

• De Boor, Carl
• Dyn, Nira
• Ron, Amos

Report Date:

1989-04-01

Pagination or Media Count:

18.0

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.

Descriptors:

• *SPLINES
• *POLYNOMIALS
• COEFFICIENTS
• DIFFERENTIAL EQUATIONS
• OPERATORS(MATHEMATICS)
• HOMOGENEITY
• DIRECTIONAL
• THEORY
• MULTIVARIATE ANALYSIS
• INTERPOLATION

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE