Maxwell operator in a cylinder with coefficients that do not depend on the cross-sectional variables

Filonov, N.

doi:10.1090/spmj/1641

Maxwell operator in a cylinder with coefficients that do not depend on the cross-sectional variables
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by N. D. Filonov
Translated by: The author

St. Petersburg Math. J. 32 (2021), 139-154

DOI: https://doi.org/10.1090/spmj/1641

Published electronically: January 11, 2021

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Abstract:

The Maxwell operator is studied in a three-dimensional cylinder whose cross-section is a simply connected bounded domain with Lipschitz boundary. It is assumed that the coefficients of the operator are scalar functions depending on the longitudinal variable only. We show that the square of such an operator is unitarily equivalent to the orthogonal sum of four scalar elliptic operators of second order. If the coefficients are periodic along the axis of the cylinder, the spectrum of the Maxwell operator is absolutely continuous.

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