On the approximation by compositions of fixed multivariate functions with univariate functions

Vugar E. Ismailov

doi:10.4064/sm183-2-2

On the approximation by compositions of fixed multivariate functions with univariate functions

Studia Mathematica ◽

10.4064/sm183-2-2 ◽

2007 ◽

Vol 183 (2) ◽

pp. 117-126 ◽

Cited By ~ 3

Author(s):

Vugar E. Ismailov

Keyword(s):

Multivariate Functions ◽

Univariate Functions

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Decomposition of Multivariate Functions

Canadian Journal of Mathematics ◽

10.4153/cjm-1992-030-9 ◽

1992 ◽

Vol 44 (3) ◽

pp. 463-482 ◽

Cited By ~ 7

Author(s):

J. M. Borwein ◽

A. S. Lewis

Keyword(s):

Existence And Uniqueness ◽

Cartesian Product ◽

Multivariate Functions ◽

Pointwise Limit ◽

Univariate Functions ◽

Bivariate Function

AbstractGiven 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.

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Tubular sets and multivariate Polya algorithm

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics ◽

10.1017/s1446788700032043 ◽

1993 ◽

Vol 55 (2) ◽

pp. 232-237 ◽

Cited By ~ 1

Author(s):

Robert Huotari

Keyword(s):

Uniform Approximation ◽

Simultaneous Approximation ◽

Multivariate Functions ◽

Best Uniform Approximation ◽

Univariate Functions

AbstractSome new results concerning tubular sets are presented, with applications to the convergence of the Polya algorithm in the contexts of simultaneous approximation and approximation of multivariate functions by univariate functions. (The Polya algorithm constructs a best uniform approximation from the limit, as p → ∞, of best Lp approximations.)

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