Extension Theorems for Spaces Arising from Approximation by Translates of a Basic Function

Authors: Light W.; Vail M.

Source: Journal of Approximation Theory, Volume 114, Number 2, February 2002 , pp. 164-200(37)

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Abstract:

We establish extension theorems for functions in spaces which arise naturally in studying interpolation by radial basic functions. These spaces are akin in some way to the non-integer-valued Sobolev spaces, although they are considerably more general. Such extensions allow us to establish local error estimates in a way which we make precise in the introductory section of our paper. There are many other applications of these fundamental results, including improved L_p error estimates for interpolation by shifts of a single basic function, but these applications have been left to a later paper. © 2001 Elsevier Science (USA)

Language: English

Document Type: Research article

Affiliations: Department of Mathematics and Computer Science, University of Leicester, Leicester, United Kingdom: