Email this article Rigorous Formulation of the Lasing Eigenvalue Problem as a Spectral Problem for a Fredholm Operator Function
- Authors: Spiridonov A.O.1, Karchevskii E.M.1, Nosich A.I.2
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Affiliations:
- Department of Applied Mathematics
- Laboratory of Micro and Nano Optics
- Issue: Vol 39, No 8 (2018)
- Pages: 1148-1157
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/203057
- DOI: https://doi.org/10.1134/S1995080218080127
- ID: 203057
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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.
About the authors
A. O. Spiridonov
Department of Applied Mathematics
Author for correspondence.
Email: aospiridonov@gmail.com
Russian Federation, ul. Kremlevskaya 18, Kazan, 420008
E. M. Karchevskii
Department of Applied Mathematics
Email: aospiridonov@gmail.com
Russian Federation, ul. Kremlevskaya 18, Kazan, 420008
A. I. Nosich
Laboratory of Micro and Nano Optics
Email: aospiridonov@gmail.com
Ukraine, vul. Proskury 12, Kharkiv, 61085
