Scattering theory with unitary twists

Author:

Doll Moritz,Fedosova Ksenia,Pohl Anke

Abstract

AbstractWe 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.

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics,Analysis

Reference19 articles.

1. D. Borthwick, C. Judge and P. Perry, Selberg’s zeta function and the spectral geometry of geometrically finite hyperbolic surfaces, Comment. Math. Helv. 80 (2005), 483–515.

2. R. Boas, Entire Functions, Academic Press, New York, 1954.

3. D. Borthwick, Spectral Theory of Infinite-area Hyperbolic Surfaces, Birkhäuser/Springer, Cham, 2016.

4. M. Doll, K. Fedosova and A. Pohl, Counting resonances on hyperbolic surfaces with unitary twists, arXiv:2109.12923 [math.SP]

5. NIST Digital Library of Mathematical Functions, Release 1.1.3 of 2021-09-15 http://dlmf.nist.gov/.

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