ON THE DISCRETENESS OF THE SPECTRUM OF INTEGRODIFFERENTIAL OPERATOR-FUNCTIONS IN THE PROBLEM OF OSCILLATIONS IN OPEN VOLUME RESONATORS
Background. The purpose of this work is to investigate the properties of the resonance frequency spectrum in the problem of oscillations of volumetric magnetodielectric resonators. Materials and methods. The study is carried out by reducing the problem to the analysis of the system of 3D integro...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Penza State University Publishing House
2020-12-01
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| Series: | Известия высших учебных заведений. Поволжский регион: Физико-математические науки |
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| Summary: | Background. The purpose of this work is to investigate the properties of the resonance
frequency spectrum in the problem of oscillations of volumetric magnetodielectric
resonators.
Materials and methods. The study is carried out by reducing the problem to the
analysis of the system of 3D integro-differential equations in the domain of heterogeneity
that determines the operator-function of the spectral parameter.
Results. We prove the theorem on the discreteness of the resonance frequency
spectrum in the problem of oscillations in volume resonators that are bounded 3D
anisotropic magneto-dielectric bodies whose permittivity and permeability functions
are piecewise smooth. The problem is reduced to the analysis of the system of
volume singular integral equations that defines a holomorphic Fredholm operatorfunction
of the spectral parameter.
Conclusions. The method of volume integro-differential equations is an effective
tool for analyzing the properties of the problem of electromagnetic oscillations of
volume magneto-dielectric resonators. |
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| ISSN: | 2072-3040 |