Rigorous Formulation of the Lasing Eigenvalue Problem as a Spectral Problem for a Fredholm Operator Function

Abstract

© 2018, Pleiades Publishing, Ltd. We propose a new convenient for mathematical investigation formulation of the lasing eigenvalue problem as a spectral problem for an operator-valued function, which involves boundary integral operators. We prove that these integral operators are weakly singular and the operator of the problem is Fredholm with index zero.