On the scattering theory of the Laplacian with a periodic boundary condition. I. Existence of wave operators
type: Item
instance of: scholarly article
title: On the scattering theory of the Laplacian with a periodic boundary condition. I. Existence of wave operators
zbMATH Open document ID: 1142.35374
author: R. L. Frank
published in: Documenta Mathematica
publication date: 2004-01-19T00:00:00Z
full work available at URL: https://eudml.org/doc/129157
full work available at URL: 16.html
review text: Summary: We study spectral and scattering properties of the Laplacian \(H^{(\sigma)} = -\Delta\) in \(L_2(\mathbb{R}^2_+)\) corresponding to the boundary condition \(\frac{\partial u}{\partial\nu} + \sigma u = 0\) for a wide class of periodic functions \(\sigma\). The Floquet decomposition leads to problems on an unbounded cell which are analyzed in detail. We prove that the wave operators \(W_\pm(H^{(\sigma)},H^{(0)})\) exist.
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 35P25
zbMATH DE Number: 2028922
zbMATH Keywords: scattering theory
zbMATH Keywords: periodic operator
zbMATH Keywords: Schrödinger operator
zbMATH Keywords: singular potential
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2028922