Claim: The Malgrande preparation theorem is an analogue of the Weierstrass preparation theorem, a tool for dealing with analytic functions of several complex variables.
Evidence: 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.