The Birman-Krein formula for differential forms and electromagnetic scattering

We consider scattering theory of the Laplace Beltrami operator on differential forms on a Riemannian manifold that is Euclidean near infinity. Allowing for compact boundaries of low regularity we prove a Birman-Krein formula on the space of co-closed differential forms. In the case of dimension thre...

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Bibliographic Details
Published inBulletin des sciences mathématiques Vol. 179; p. 103166
Main Authors Strohmaier, Alexander, Waters, Alden
Format Journal Article
LanguageEnglish
Published Elsevier Masson SAS 01.10.2022
Subjects
Birman-Krein formula
Differential forms
Obstacle scattering
Scattering theory on manifolds
Birman-Krein formula
Differential forms
Obstacle scattering
Scattering theory on manifolds
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Summary:We consider scattering theory of the Laplace Beltrami operator on differential forms on a Riemannian manifold that is Euclidean near infinity. Allowing for compact boundaries of low regularity we prove a Birman-Krein formula on the space of co-closed differential forms. In the case of dimension three this reduces to a Birman-Krein formula in Maxwell scattering.
ISSN:0007-4497
1952-4773
DOI:10.1016/j.bulsci.2022.103166