年間 12 号発行
ISSN 印刷: 0040-2508
ISSN オンライン: 1943-6009
Indexed in
PROPERTIES OF SOME MATRIX OPERATORS APPEARING IN THE THEORY OF PLANAR WAVEGUIDE JUNCTIONS
要約
In the paper infinite sets of linear equations are investigated which arise in the course of applying the domainâ€product technique to analyzing flatâ€bed waveguide transformers with a convexâ€polygonal junction plane. Blocks of the system matrix describing the interaction of sides of the polygon are considered in the capacity of operators in the sequence space l1. It is shown that each operator of the kind for adjacent sides can be represented as a sum of a completely continuous operator and the contraction operator. Results of the study are used to justify the solvability by the reduction technique of systems corresponding to the triangular region. It is proved the set of matrix equations arising in the case of an Еâ€plane structure can be considered in the space l1(3) = l1 ⊕ l1 ⊕ l1 in the capacity of a functional equation with the Fredholm operator. It is shown that this equation can be solved by the projection technique convergent in the norm of the mentioned space. Similar results are obtained in the case of the Ðâ€plane problem.
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Chumachenko V. P., On DPT representations of solutions to the Helmholtz equation in a convex N-gon, 2014 International Conference on Mathematical Methods in Electromagnetic Theory, 2014. Crossref
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Bulashenko Andrew, Piltyay Stepan, Dikhtyaruk Ivan, Bulashenko Oleksandr, FDTD and wave matrix simulation of adjustable DBS-band waveguide polarizer, Journal of Electromagnetic Waves and Applications, 36, 6, 2022. Crossref