Characterizations of Native Spaces

Abstract

In the theory of radial basis functions, linear combinations of the translates of a single function Phi are used as interpolants. The space spanned by all of these linear combinations carries an inner product defined via Phi itself. It can be completed and becomes a Hilbert space, called the native space for Phi, which is of great importance for further investigation of radial basis functions. The native space will contain abstract elements which are not linear combinations of radial basis functions, and require some work to be recognized as functions. This paper provides some characterizations of native spaces and relates some of the different approaches used to define them. Finally, embedding results for native spaces into Sobolev spaces are proven.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2000
Accession Number
ADP011998

Entities

People

  • Lin Tian Luh

Organizations

  • Providence University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Construction
  • Embedding
  • Equations
  • Hilbert Space
  • Polynomials
  • Technical Information Centers
  • Topology
  • Variational Equations

Fields of Study

  • Mathematics

Readers

  • Aerospace Engineering.
  • Calculus or Mathematical Analysis
  • Systems Analysis and Design

Technology Areas

  • Space