DOI

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.

Original languageEnglish
Pages (from-to)139-154
JournalSt. Petersburg Mathematical Journal
Volume32
Issue number1
DOIs
StatePublished - 11 Jan 2021

    Research areas

  • absolute continuity of the spectrum, Maxwell operator, simply connected cylinder

    Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

ID: 91106800