Oscillatory integral operator

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

Source: Wikipedia — Oscillatory integral operator (CC BY-SA 4.0)