The Malgrande preparation theorem is an analogue of the Weierstrass preparation theorem, a tool for dealing with analytic functions of several complex variables.
In mathematics, the Malgrange preparation theorem is an analogue of the Weierstrass preparation theorem for smooth functions. 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 of lower degree terms are analytic functions in the remaining variables and zero at P. 
