Decomposition of Multivariate Functions
Decomposition of Multivariate Functions
复制标题
多元函数的分解
DOI：
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发表时间：
1992
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通讯作者：
Adrian S. Lewis
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作者：
J. M. Borwein;Adrian S. Lewis
给定一个定义在两个集合的笛卡尔积的某个子集上的二元函数，很自然地会问这个函数何时可以分解为两个一元函数的和。特别是，是一个逐点限制这样的功能本身可分解？乍一看，这似乎显然是正确的，但正如我们所展示的，可能性是相当微妙的。我们认为这种情况下，许多推广到多元函数和情况下，集合和功能的拓扑或测度理论结构的分解的存在性和唯一性的问题。
Abstract 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.