Gaussian, we obtain a well known sequence of functions which approximate the delta function: An operator in this case is given for example by where is the Laplacian with respect to the variables, and is any integer greater than . Indeed, with this we have and this integral converges absolutely. The Schwartz kernel of any differential operator can be written as an oscillatory integral. Indeed if where , then the kernel of is given by Relation to Lagrangian distributions Any Lagrangian distribution can be represented locally by oscillatory integrals, see . Conversely, any oscillatory integral is a Lagrangian distribution. This gives a precise description of the types of distributions which may be represented as oscillatory integrals. See also Riemann–Lebesgue lemma van der Corput lemma References Mathematical analysis Generalized functions Functional analysis