Oscillatory integral operator

An oscillatory integral operator is a mathematical object that arises in the analysis of oscillatory integrals, which are integrals of the form: \[ I(f)(x) = \int_{\mathbb{R}^n} e^{i\phi(x, y)} f(y) \, dy \] where: - \(I\) is the operator being defined, - \(f\) is a function (often a compactly supported or suitable function), - \(x\