Limiting amplitude principle (original) (raw)

In mathematics, the limiting amplitude principle is a concept from operator theory and scattering theory used for choosing a particular solution to the Helmholtz equation. The choice is made by considering a particular time-dependent problem of the forced oscillations due to the action of a periodic force.The principle was introduced by Andrey Nikolayevich Tikhonov and Alexander Andreevich Samarskii.It is closely related to the limiting absorption principle (1905) and the Sommerfeld radiation condition (1912).The terminology -- both the limiting absorption principle and the limiting amplitude principle -- was introduced by Aleksei Sveshnikov.