Weierstrass Preparation Theorem
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High Quality Content by WIKIPEDIA articles! In mathematics, the Weierstrass preparation theorem is a tool for dealing with analytic functions of several complex variables, at a given point P. It states that such a function is, up to multiplication by a function not zero at P, a polynomial in one fixed variable z, which is monic, and whose coefficients are analytic functions in the remaining variables and zero at P. There are also a number of variants of the theorem, that extend the idea of factorization in some ring R as u.w, where u is a unit and w is some sort of distinguished Weierstrass po...
High Quality Content by WIKIPEDIA articles! In mathematics, the Weierstrass preparation theorem is a tool for dealing with analytic functions of several complex variables, at a given point P. It states that such a function is, up to multiplication by a function not zero at P, a polynomial in one fixed variable z, which is monic, and whose coefficients are analytic functions in the remaining variables and zero at P. There are also a number of variants of the theorem, that extend the idea of factorization in some ring R as u.w, where u is a unit and w is some sort of distinguished Weierstrass polynomial. C.L. Siegel has disputed the attribution of the theorem to Weierstrass, saying that it occurred under the current name in some of late nineteenth century Traités d'analyse without justification.
