Geodesic
Decomposition of Multivariate Functions
Canadian journal of mathematics, Tome 44 (1992) no. 3, pp. 463-482

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-1992-030-9
Mots-clés : 54C05, 05C38, 08A45, 28A20, Separable function, conservative, potential difference, equational compactness 
Borwein, J. M.; Lewis, A. S. Decomposition of Multivariate Functions. Canadian journal of mathematics, Tome 44 (1992) no. 3, pp. 463-482. doi: 10.4153/CJM-1992-030-9
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