On Limits of Multivariate B-Splines.

Abstract

B-splines occupy a pivotal position in the theory of univariate spline functions. They offer a firm bases for many of the attractive theoretical and practical properties of splines. Therefore any advance in our knowledge concerning the multivariate B-spline should be of some value. The purpose of this paper is to investigate another aspects of multivariate B-splines. We succeed in identifying those distribution functions which are limits of multivariate B-splines (Polya distributions). This question was solved in one dimension by Curry and Schoenberg. Some properties of Polya distributions on Rs are also discussed.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1980
Accession Number
ADA093628

Entities

People

  • Charles A. Micchelli
  • Wolfgang Dahmen

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Analytic Functions
  • Convergence
  • Distribution Functions
  • Equations
  • Frequency
  • Functions (Mathematics)
  • Gaussian Distributions
  • Identities
  • Inequalities
  • Laguerre Functions
  • Mathematical Analysis
  • Mathematics
  • Numerical Analysis
  • Polynomials
  • Probability
  • Probability Distributions
  • United States

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Systems Analysis and Design