The Existence of Eigenvalues for the Integral Equations of Laser Theory

Homogeneous linear Fredholm integral equations with nonsingular kernels of normal type (which includes Hermitian kernels as a special case), i.e., kernels for which have been extensively studied. Within the framework of complex-valued £2 functions, questions of existence, uniqueness, and representation of 77 78 T H E BELL SYSTEM TECHNICAL J O U R N A L , JANUARY 1965 solutions can be largely answered for such equations. Recently, however, a number of integral equations involving kernels which are neither Hermitian nor normal have arisen in laser theory. These kernels, of which K(x,y) = e ^ 2 , (1)