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Trigonometric and cylindrical polynomials and their applications in electromagnetics
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
2019 (English)In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504XArticle in journal (Refereed) Epub ahead of print
Abstract [en]

Development of the theory of trigonometric polynomials (TPs) is considered that involves generalization of the notion of TP and extension of the methods and results to cylindrical polynomials (CPs). On the basis of the proposed augmentation of TPs and CPs, a general approach is presented to the analysis of guided waves and resonances in electromagnetics and beyond. The method employs the known explicit forms of dispersion equations (DEs) describing eigenoscillations and normal waves in layered structures and is based on the development of the theory of generalized TPs and CPs performed in the study. The approach enables one to complete rigorous proofs of existence and determine domains of localization of the TP and CP zeros and the DE roots and validate iterative numerical solution techniques.

Place, publisher, year, edition, pages
Taylor & Francis , 2019.
Keywords [en]
cylindrical polynomials; dispersion equation; zeros; electromagnetic waves
National Category
Mathematics Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:hig:diva-30485DOI: 10.1080/00036811.2019.1584290Scopus ID: 2-s2.0-85062349423OAI: oai:DiVA.org:hig-30485DiVA, id: diva2:1341843
Available from: 2019-08-12 Created: 2019-08-12 Last updated: 2019-08-12Bibliographically approved

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Shestopalov, Yury

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