2019/09/13 by Jian Wang, Wang, Jian · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1909.06484
openalex publication_date 2019/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We use microlocal radial estimates to prove the full limiting absorption principle for P, a self-adjoint 0th order pseudodifferential operator satisfying hyperbolic dynamical assumptions as of Colin de Verdière and Saint-Raymond. We define the scattering matrix for P-ω with generic ω∈ \mathbb R and show that the scattering matrix extends to a unitary operator on appropriate L2 spaces. After conjugation with natural reference operators, the scattering matrix becomes a 0th order Fourier integral operator with a canonical relation associated to the bicharacteristics of P-ω. The operator P gives a microlocal model of internal waves in stratified fluids as illustrated in the paper of Colin de Verdière and Saint-Raymond.