 Limiting absorption principle

Select outgoing waves as a limit of a problem with weak absorption. With time convention $e^{-i\omega t}$ use $\mathrm{Im}\omega >0$; with $e^{i\omega t}$ use $\mathrm{Im}\omega <0$. The resulting Green function and transform-contour prescriptions determine which poles represent incoming or outgoing waves. This is especially useful when real-axis singularities obscure a Wiener-Hopf factorization.

The Limiting Absorption Principle (LAP) is a concept in the field of mathematical physics, particularly in the study of differential operators and partial differential equations. It relates to the analysis of the resolvent of an operator, which is a tool used to understand the behavior of solutions to differential equations. The LAP states that, under certain conditions, the resolvent operator of a differential operator can be defined and its limit can be taken as a parameter approaches the continuous spectrum.