Glaeser's composition theorem

In mathematics, Glaeser's theorem, introduced by Georges Glaeser (1963), is a theorem giving conditions for a smooth function to be a composition of F and θ for some given smooth function θ. One consequence is a generalization of Newton's theorem that every symmetric polynomial is a polynomial in the elementary symmetric polynomials, from polynomials to smooth functions.

References

• Glaeser, Georges (1963), "Fonctions composées différentiables", Annals of Mathematics, Second Series 77 (1): 193–209, doi:10.2307/1970204, http://www.numdam.org/item/SL_1962-1963__5__A2_0/