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

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

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 Fre...

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Veröffentlicht in:Lobachevskii journal of mathematics 2018-10, Vol.39 (8), p.1148-1157
Hauptverfasser: Spiridonov, A. O., Karchevskii, E. M., Nosich, A. I.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Analysis
Eigenvalues
Geometry
Integrals
Lasing
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Matrix
Operators (mathematics)
Probability Theory and Stochastic Processes
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Zusammenfassung: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.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080218080127