Scattering theory with unitary twists

We study the spectral properties of the Laplace operator associated to a hyperbolic surface in the presence of a unitary representation of the fundamental group. Following the approach by Guillopé and Zworski, we establish a factorization formula for the twisted scattering determinant and describe t...

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Bibliographic Details
Published inJournal d'analyse mathématique (Jerusalem) Vol. 153; no. 1; pp. 111 - 167
Main Authors Doll, Moritz, Fedosova, Ksenia, Pohl, Anke
Format Journal Article
LanguageEnglish
Published Jerusalem The Hebrew University Magnes Press 01.09.2024
Springer Nature B.V
Subjects
Abstract Harmonic Analysis
Analysis
Dynamical Systems and Ergodic Theory
Functional Analysis
Laplace transforms
Mathematics
Mathematics and Statistics
Operators (mathematics)
Partial Differential Equations
S matrix theory
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Summary:We study the spectral properties of the Laplace operator associated to a hyperbolic surface in the presence of a unitary representation of the fundamental group. Following the approach by Guillopé and Zworski, we establish a factorization formula for the twisted scattering determinant and describe the behavior of the scattering matrix in a neighborhood of 1/2.
ISSN:0021-7670
1565-8538
DOI:10.1007/s11854-023-0313-0