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Small degree solutions for the polynomial Bezout equation. (English) Zbl 0643.13006

As it follows from the Nullstellensatz, if n-variate polynomials \(P_ 1,...,P_ m\) have no common zeros in \({\mathbb{C}}^ n\) then \((1)\quad P_ 1Q_ 1+...+P_ mQ_ m=1\) for appropriate \(Q_ 1,...,Q_ m\). - The paper under review contains an overview of ideas for explicit construction of such \(Q_ i\) of smallest possible degree. It is noted that by the Fourier transformation (1) is equivalent to the important convolution equation \(\mu_ 1*\nu_ 1+...+\mu_ m*\nu_ m=\delta\).
Reviewer: A.V.Bocharev

MSC:

13F20 Polynomial rings and ideals; rings of integer-valued polynomials
32A05 Power series, series of functions of several complex variables
12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems)
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References:

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