Symbol of the Dirichlet-to-Neumann operator in 2D diffraction problems with large wavenumber

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/85639We put forward a conjecture about an universal asymptotical behaviour of the symbol of the Dirichlet-to-Neumann operator (considered as a pseudodifferential operator) in the 2D exterior problem for the Hemholtz equation. The conjecture is motivated by simple explicit examples and backed by numerical calculations, even in the case of a non-convex obstacle. It implies (at a physical level of rigor) Kirhhoff's approximation.10 pages, 4 figures, LaTeX/ps, talk at the conference "Days on Diffractions'03", St.Petersburg, Russia, June 2003OpticsComputational PhysicsSymbol of the Dirichlet-to-Neumann operator in 2D diffraction problems with large wavenumbertext