Is there any result about oscillatory integrals of the form$$I=\int_{0}^{\infty}e^{inx}f(x)dx$$
I know by Van der Corput Lemma that $|I|\leq c\frac{1}{n}$ for some constant $c>0$.
Can one get higher-order corrections?Any help will be appreciated
Is there any result about oscillatory integrals of the form$$I=\int_{0}^{\infty}e^{inx}f(x)dx$$
I know by Van der Corput Lemma that $|I|\leq c\frac{1}{n}$ for some constant $c>0$.
Can one get higher-order corrections?Any help will be appreciated