A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is `application/pdf`

.

##
###
The notion of approximate eigenvalues applied to an integral equation of laser theory

1977
*
Quarterly of Applied Mathematics
*

The integral operator with kernel (iri/ir)1'2 exp [-it)(x -yf] on the interval \x\, y < 1 serves to model the behavior of a class of lasers. Although the kernel is simple, it is not Hermitian; this presents a major obstacle to a theoretical understanding of the equation-indeed, even the existence of eigenvalues is difficult to prove. We here introduce a definition of approximate eigenvalues and eigenfunctions, and argue that these will model the physical problem equally well. We then show that,

doi:10.1090/qam/446101
fatcat:tdijgbd7njethkwhz52tify7re