Abstract
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.
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Spiridonov, A.O., Karchevskii, E.M. & Nosich, A.I. Rigorous Formulation of the Lasing Eigenvalue Problem as a Spectral Problem for a Fredholm Operator Function. Lobachevskii J Math 39, 1148–1157 (2018). https://doi.org/10.1134/S1995080218080127
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DOI: https://doi.org/10.1134/S1995080218080127