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Telecommunications and Radio Engineering
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ISSN Imprimer: 0040-2508
ISSN En ligne: 1943-6009

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Telecommunications and Radio Engineering

DOI: 10.1615/TelecomRadEng.v67.i19.10
pages 1701-1709

Abrupt Discontinuities: The Reflection Operator is a Contraction

I. V. Petrusenko
A. Usikov Institute of Radio Physics and Electronics, National Academy of Sciences of Ukraine; University of Customs Affair and Finances, 8, Rogaleva St., Dnepropetrovsk 49000, Ukraine
Yurii Konstantinovich Sirenko
O.Ya. Usikov Institute for Radio Physics and Electronics, National Academy of Sciences of Ukraine, 12, Academician Proskura St., Kharkiv 61085, Ukraine; V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv 61022, Ukraine; L.N. Gumilyov Eurasian National University, 2, Satpayev St., Astana 010008, Republic of Kazakhstan

RÉSUMÉ

New basic properties of the reflection operator are analyzed for the problem of wave diffraction by abrupt discontinuities. A generalized (operator) form of the power conservation statement has been used to evaluate the norm of this operator and investigate the localization and the structure of its spectrum. The results obtained are useful for justifying matrix models of the considered class of diffraction problems, as well as for developing new methods of electrodynamic analysis of waveguiding and periodic structures.


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