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Asymptotics for oscillatory integral
Consider the following integral for $f \in C_c^{\infty}(\mathbb R^n)$, $x_0$ fixed (possibly zero), and $n \ge 3$
$$F(\lambda) = \int_{\mathbb R^n} e^{i\lambda \vert x-x_0 \vert^2} \frac{f(x)}{\vert x …