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Decomposition of Multivariate Functions

Published online by Cambridge University Press:  20 November 2018

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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1992

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