Reconstructing a function from its values on a subset of its domain - a Hilbert space approach
type: Item
instance of: scholarly article
title: Reconstructing a function from its values on a subset of its domain - a Hilbert space approach
zbMATH Open document ID: 0594.41021
DOI: 10.1016/0021-9045(86)90072-9
author: H. S. Shapiro
published in: Journal of Approximation Theory
publication date: 1986-01-01T00:00:00Z
review text: This paper, which should be regarded as mainly expository, presents the general features of a reconstruction (or extrapolation) procedure, various cases of which have been discussed in the literature. The main idea is that the restrictions of functions in a suitable Hilbert space H of functions on a set E, to a subset \(E_ 0\), can be recognized and in principle extrapolated to E, in terms of the spectral resolution of a certain self-adjoint operator on H that can be introduced (in the presence of some natural hypotheses). Examples are given. It has been pointed out to the author that the general results can be obtained from the extant theory of solving ''ill posed problems'' by the method of Tikhonov regularization.
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 30E10
zbMATH DE Number: 3955653
zbMATH Keywords: reconstruction
zbMATH Keywords: extrapolation
zbMATH Keywords: Hilbert space
zbMATH Keywords: self-adjoint operator
zbMATH Keywords: Examples
zbMATH Keywords: ill posed problems
MaRDI profile type: Publication
full work available at URL: 0021-9045(86)90072-9
OpenAlex ID: W1981940744
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description: scientific article; zbMATH DE number 3955653