Commutator methods and a smoothing property of the Schrödinger evolution group
type: Item
instance of: scholarly article
title: Commutator methods and a smoothing property of the Schrödinger evolution group
zbMATH Open document ID: 0594.35032
DOI: 10.1007/BF01163609
author: Arne Jensen
published in: Mathematische Zeitschrift
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173656
review text: Let \(H=-()\Delta +V\) be a Schrödinger operator in \(L^ 2(R^ n)\), where V is a real-valued function, which satisfies the condition \((\partial /\partial x)^{\alpha}V\in L^{\infty}(R^ n)\) for \(| \alpha | \leq k\), where k is a given integer. The main result is the following smoothing property of the unitary evolution group: For \(t\neq 0\) \((1+x^ 2)^{-k/2}e^{-itH}(1+x^ 2)^{-k/2}\) is bounded from \(L^ 2(R^ n)\) to the Sobolev space \(H^ k(R^ n)\). The proof uses the boost group \(e^{iax}\), \(a\in R^ n\), and commutator methods. There is a misprint in formula (2.4) in Lemma 2.2: In the integral (t-s) should be replaced by s.
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 47F05
zbMATH DE Number: 3955530
zbMATH Keywords: Schrödinger operator
zbMATH Keywords: smoothing property
zbMATH Keywords: unitary evolution group
zbMATH Keywords: Sobolev space
zbMATH Keywords: boost group
zbMATH Keywords: commutator methods
MaRDI profile type: Publication
cites work: On the Space-Time Behavior of Schrödinger Wavefunctions
cites work: Q4110164
cites work: Propagation of states in dilation analytic potentials and asymptotic completeness
cites work: Schrödinger semigroups
cites work: Uniform Asymptotic Estimates for Wave Packets in the Quantum Theory of Scattering
description: scientific article; zbMATH DE number 3955530