Transmission eigenvalues and the Riemann zeta function in scattering theory for automorphic forms on Fuchsian groups of type I

DOI10.1007/S10114-019-8128-8zbMath1444.11103OpenAlexW2946433843WikidataQ127815999 ScholiaQ127815999MaRDI QIDQ2311725

Fioralba Cakoni, Sagun Chanillo

Publication date: 4 July 2019

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-019-8128-8

zbMATH Keywords

Riemann zeta functionscattering theorytransmission eigenvaluesfuchsian groups

Mathematics Subject Classification ID

Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46) Scattering theory, inverse scattering involving ordinary differential operators (34L25)

Related Items (1)

On corner scattering for operators of divergence form and applications to inverse scattering

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Corners always scatter
• On cusp forms for co-finite subgroups of PSL(2,\({\mathbb{R}})\)
• The Selberg trace formula for \(\text{PSL}(2,\mathbb R)\). Vol. 2
• Dimension of the limit set and the density of resonances for convex co-compact hyperbolic surfaces
• Scattering asymptotics for Riemann surfaces
• High-frequency approximation of the interior Dirichlet-to-Neumann map and applications to the transmission eigenvalues
• The interior transmission problem and bounds on transmission eigenvalues
• Inverse Scattering Theory and Transmission Eigenvalues
• The existence of complex transmission eigenvalues for spherically stratified media
• The Existence of an Infinite Discrete Set of Transmission Eigenvalues
• Stochastic stability of Pollicott–Ruelle resonances
• Scattering theory for automorphic functions
• Scattering Theory for Automorphic Functions. (AM-87)
• Parabolic transmission eigenvalue-free regions in the degenerate isotropic case
• Distribution of complex transmission eigenvalues for spherically stratified media
• Remarks on interior transmission eigenvalues, Weyl formula and branching billiards
• Spectral analysis of the interior transmission eigenvalue problem
• Complex eigenvalues and the inverse spectral problem for transmission eigenvalues
• The inside–outside duality for scattering problems by inhomogeneous media
• Invisibility and inverse problems
• Inverse acoustic and electromagnetic scattering theory
• Spectral theory of infinite-area hyperbolic surfaces

This page was built for publication: Transmission eigenvalues and the Riemann zeta function in scattering theory for automorphic forms on Fuchsian groups of type I