Spectral and scattering properties at thresholds for the Laplacian in a half-space with a periodic boundary condition

2014/12/02 by Serge Richard, Richard, S., Rafael Tiedra de Aldecoa +1 · 1 citation
Mathematics · #Spectral Theory in Mathematical Physics #Numerical methods in inverse problems #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1412.0990

Abstract

For the scattering system given by the Laplacian in a half-space with a periodic boundary condition, we derive resolvent expansions at embedded thresholds, we prove the continuity of the scattering matrix, and we establish new formulas for the wave operators.

Cited by

• Topological Levinson's theorem and corrections at thresholds: the full picture in a quasi-1D example

Related

• Discrete Laplacian in a half-space with a periodic surface potential I: Resolvent expansions, scattering matrix, and wave operators
• Resolvent expansions and continuity of the scattering matrix at embedded thresholds: the case of quantum waveguides
• Structure of the Short Range Amplitude for General Scattering Relations
• Resolvent expansions for the Schrödinger operator on the discrete half-line
• Wave Operators for Schrödinger Operators with Threshold Singuralities, Revisited