In mathematics, in the field of harmonic analysis, an oscillatory integral operator is an integral operator of the form T λ u = ∫ R n e i λ S a u d y, x ∈ R m, y ∈ R n, {\displaystyle T_{\lambda }u=\int _{\mathbb {R} ^{n}}e^{i\lambda S}au\,dy,\qquad x\in \mathbb {R} ^{m},\quad y\in \mathbb {R} ^{n},} where the function S is called the phase of the operator and the function a is called the symbol of the operator. Wikipedia