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Decomposition of Multivariate Functions

Published online by Cambridge University Press:  20 November 2018

J. M. Borwein  and
A. S. Lewis
J. M. Borwein
Affiliation:
Department of Combinatorics & Optimization University of Waterloo Waterloo, OntarioN2L 3GI
A. S. Lewis
Affiliation:
Department of Combinatorics & Optimization University of Waterloo Waterloo, OntarioN2L 3GI
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Abstract

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Given a bivariate function defined on some subset of the Cartesian product of two sets, it is natural to ask when that function can be decomposed as the sum of two univariate functions. In particular, is a pointwise limit of such functions itself decomposable? At first glance this might seem obviously true but, as we show, the possibilities are quite subtle. We consider the question of existence and uniqueness of such decompositions for this case and for many generalizations to multivariate functions and to cases where the sets and functions have topological or measure theoretic structure.

Keywords

54C0505C3808A4528A20Separable functionconservativepotential differenceequational compactness
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 3 , 01 June 1992 , pp. 463 - 482
Copyright
Copyright © Canadian Mathematical Society 1992

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