On the scattering theory of the Laplacian with a periodic boundary condition. II. Additional channels of scattering
type: Item
instance of: scholarly article
title: On the scattering theory of the Laplacian with a periodic boundary condition. II. Additional channels of scattering
zbMATH Open document ID: 1210.35040
author: R. L. Frank
author: Roman Shterenberg
published in: Documenta Mathematica
publication date: 2004-08-31T00:00:00Z
full work available at URL: https://eudml.org/doc/44744
full work available at URL: 04.html
review text: The authors study the Laplacian \[ H^{(\sigma)}u= -\Delta u\quad\text{on }\mathbb{R}^2_+ \] together with a boundary condition of the third type \[ {\partial u\over\partial\nu}+ \sigma u= 0\quad\text{on }\mathbb{R}\times \{0\}, \] where \(\nu\) denotes the exterior unit normal and where the function \(\sigma: \mathbb{R}\to\mathbb{R}\) is assumed to be \(2\pi\)-periodic. The authors prove that for nonnegative \(\sigma\), \(H^{(\sigma)}\) is unitary equivalent to the Neumann-Laplacian \(H^{(0)}\). For part I, cf. ibid. 8, 547--565 (2003; Zbl 1142.35374).
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 35P25
zbMATH DE Number: 2095717
zbMATH Keywords: scattering theory
zbMATH Keywords: unitary equivalence
zbMATH Keywords: periodic boundary condition
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2095717