The eigenfunction problem in higher dimensions: Asymptotic theory.
The spectral problem for linear operators on fully infinite domains is considered. A transformation first introduced by Wigner is used to show a number of asymptotic results. The method leads to a WKB (Wentzel-Kromers-Brillouin) theory for operators in more than one dimension. This includes practical tools for the approximate evaluation of spectra and eigenfunctions. Several general examples are developed.
Sirovich
L
L
Brown University, Providence, RI 02912.
Knight
B W
BW