Multivariate polynomials: A spanning question |
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Authors: | A Pinkus B Wajnryb |
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Institution: | 1. Department of Mathematics, Technion, 32000, Haifa, Israel 2. Department of Mathematics, Technion, 32000, Haifa, Israel
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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. |
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