Scattering and spectral theory for the linear Boltzmann operator
type: Item
instance of: scholarly article
title: Scattering and spectral theory for the linear Boltzmann operator
zbMATH Open document ID: 0558.47009
author: Tomio Umeda
published in: Journal of Mathematics of Kyoto University
publication date: 1984-01-01T00:00:00Z
review text: This paper is concerned with the linear Boltzmann operator (transport operator) in multiple scattering problem in \(L^ 1\)-space. Scattering theory for the linear Boltzmann operator is studied by the Enss method. The author deals only with the inverse wave operator \(\tilde W_+=- \lim_{t\to \infty}e^{tB_ 0}e^{-tB},\) where \(-B_ 0\) and -B are the collisionless Boltzmann operator and the linear Boltzmann operator respectively. He shows that the range of \(\tilde W_+\) is dense in \(L^ 1\). By exploiting this result, he investigates also the spectrum of the operator B. This paper shows that the Enss method is a useful tool in scattering theory even in Banach space, and that scattering theory in Banach space, as well as in Hilbert space, is closely related to spectral theory.
Mathematics Subject Classification ID: 47A40
Mathematics Subject Classification ID: 35P25
zbMATH DE Number: 3890181
zbMATH Keywords: linear Boltzmann operator
zbMATH Keywords: transport operator
zbMATH Keywords: multiple scattering problem in \(L^ 1\)-space
zbMATH Keywords: Enss method
zbMATH Keywords: inverse wave operator
zbMATH Keywords: collisionless Boltzmann operator
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250521324
OpenAlex ID: W1599337485
DOI: 10.1215/KJM/1250521324
description: scientific article; zbMATH DE number 3890181