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Multivariate polynomials: A spanning question (1995)

Pinkus, A. ; Wajnryb, B.

Springer

Constructive approximation 11 (1995), S. 165-180

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ISSN: 1432-0940

Keywords: 41A10 ; 41A63 ; Multivariate polynomials ; Spanning set

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract The main result of this paper is the following. Ifg is any given polynomial of two variables, then $$span\left\{ {\left( {g\left( {. - a,. - b} \right)} \right)^k :\left( {a,b} \right) \in R^2 ,k \in {\rm Z}_ + } \right\}$$ contains all polynomials if and only if $$span\left\{ {g\left( {. - a,. - b} \right):\left( {a,b} \right) \in R^2 } \right\}$$ separates points. This result is not valid inR d ford≥4.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01203414

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