Schrödinger semigroups on the scale of Sobolev spaces
type: Item
instance of: scholarly article
title: Schrödinger semigroups on the scale of Sobolev spaces
zbMATH Open document ID: 0594.46025
published in: Pacific Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: The author considers the smoothing properties of Schrödinger semigroups \(e^{-tH}\) with \(H=\Delta +V\) on \(L^ 2(R^{\nu})\), on the scale of Sobolev spaces \({\mathcal H}\), and show that while \(e^{-tH}\) maps \(L^ 2={\mathcal H}^ 0\) to \({\mathcal H}^ 2\), there exist bounded V so that for all \(\beta >0\), \(e^{-tH}[{\mathcal H}]\) is not contained in any \({\mathcal H}^{\alpha}\) with \(\alpha >2\).
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 35J10
zbMATH DE Number: 3955719
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: imbedding theorems
zbMATH Keywords: smoothing properties of Schrödinger semigroups
zbMATH Keywords: scale of Sobolev spaces
author: B. Simon
MaRDI profile type: Publication
full work available at URL: pjm.1986.122.475
OpenAlex ID: W2113439241
DOI: 10.2140/PJM.1986.122.475
description: scientific article; zbMATH DE number 3955719