Maxwell Operator in a Cylinder with Coefficients that do not Depend on the Cross-Sectional Variables

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Maxwell Operator in a Cylinder with Coefficients that do not Depend on the Cross-Sectional Variables. / Filonov, N. D.

In: St. Petersburg Mathematical Journal, Vol. 32, No. 1, 11.01.2021, p. 139-154.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{2a702ff75ca645f182951212b58ca0e8,

title = "Maxwell Operator in a Cylinder with Coefficients that do not Depend on the Cross-Sectional Variables",

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.",

keywords = "absolute continuity of the spectrum, Maxwell operator, simply connected cylinder",

author = "Filonov, {N. D.}",

year = "2021",

month = jan,

day = "11",

doi = "10.1090/SPMJ/1641",

language = "English",

volume = "32",

pages = "139--154",

journal = "St. Petersburg Mathematical Journal",

issn = "1061-0022",

publisher = "American Mathematical Society",

number = "1",

}

RIS

TY - JOUR

T1 - Maxwell Operator in a Cylinder with Coefficients that do not Depend on the Cross-Sectional Variables

AU - Filonov, N. D.

PY - 2021/1/11

Y1 - 2021/1/11

N2 - 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.

AB - 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.

KW - absolute continuity of the spectrum

KW - Maxwell operator

KW - simply connected cylinder

UR - http://www.scopus.com/inward/record.url?scp=85100014719&partnerID=8YFLogxK

U2 - 10.1090/SPMJ/1641

DO - 10.1090/SPMJ/1641

M3 - Article

AN - SCOPUS:85100014719

VL - 32

SP - 139

EP - 154

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 1

ER -

ID: 91106800