Rigorous Formulation of the Lasing Eigenvalue Problem as a Spectral Problem for a Fredholm Operator Function
- Авторы: Spiridonov A.1, Karchevskii E.1, Nosich A.2
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Учреждения:
- Department of Applied Mathematics
- Laboratory of Micro and Nano Optics
- Выпуск: Том 39, № 8 (2018)
- Страницы: 1148-1157
- Раздел: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/203057
- DOI: https://doi.org/10.1134/S1995080218080127
- ID: 203057
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Аннотация
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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Об авторах
A. Spiridonov
Department of Applied Mathematics
Автор, ответственный за переписку.
Email: aospiridonov@gmail.com
Россия, ul. Kremlevskaya 18, Kazan, 420008
E. Karchevskii
Department of Applied Mathematics
Email: aospiridonov@gmail.com
Россия, ul. Kremlevskaya 18, Kazan, 420008
A. Nosich
Laboratory of Micro and Nano Optics
Email: aospiridonov@gmail.com
Украина, vul. Proskury 12, Kharkiv, 61085