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Resonance frequencies of arbitrarily shaped dielectric cylinders
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.ORCID iD: 0000-0002-2691-2820
2023 (English)In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 102, no 6, p. 1618-1632Article in journal (Refereed) Published
Abstract [en]

We consider eigenvalue problems for dielectric cylindrical scatterers of arbitrary cross section with generalized conditions at infinity that enable one to take into account complex eigenvalues. The existence of resonance (scattering) frequencies associated with these eigenvalues is proved. The technique involves the determination of characteristic numbers (CNs) of the Fredholm operator-valued functions of the problems constructed using Green's potentials. Separating principal parts in the form of meromorphic operator pencils, we apply the operator generalization of Rouché's theorem to verify the occurrence of CNs in close proximities of the pencil poles. The results are illustrated in detail using the case of a dielectric cylinder of circular cross section.

Place, publisher, year, edition, pages
Taylor & Francis, 2023. Vol. 102, no 6, p. 1618-1632
Keywords [en]
Resonance frequencies; boundary integral equations; operator-valued functions; finite-meromorphic pole pencils
National Category
Mathematics
Identifiers
URN: urn:nbn:se:hig:diva-37170DOI: 10.1080/00036811.2021.1992397ISI: 000707609900001Scopus ID: 2-s2.0-85117192532OAI: oai:DiVA.org:hig-37170DiVA, id: diva2:1603568
Available from: 2021-10-15 Created: 2021-10-15 Last updated: 2023-06-16Bibliographically approved

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Shestopalov, Yury

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard-cite-them-right
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • sv-SE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • de-DE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf