Global smoothing properties of generalized Schrödinger equations
type: Item
instance of: scholarly article
title: Global smoothing properties of generalized Schrödinger equations
zbMATH Open document ID: 0928.35138
DOI: 10.1007/BF02786935
author: Mitsuru Sugimoto
published in: Journal d'Analyse Mathématique
publication date: 1999-11-02T00:00:00Z
review text: The author proves regularity results of type `decay implies smoothing' for the free homogeneous and inhomegeneous time-dependent Schrödinger equation, for more general equations of similar type, and also for linear problems of wave equation type. The results are generalizations of earlier ones of the same type by Constantin and Saut, Kato and Yajima, Kenig, Ponce and Vega, and others. The proofs crucially use refined resolvent estimates (proved by the author and T. Tsujimoto) for the linear differential operator involved in the equations, weighted Hardy spaces, and restriction type theorems.
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 1274829
zbMATH Keywords: linear time-dependent Schrödinger equations
reviewed by: Horst Lange
MaRDI profile type: Publication
cites work: Local smoothing and convergence properties of Schrödinger type equations
cites work: Decay and regularity for the Schrödinger equation
cites work: Local Smoothing Properties of Dispersive Equations
cites work: Q3671564
cites work: On weighted \(L^2\) estimates of solutions to wave equations
cites work: On the estimates for Helmholtz operator
cites work: Commutator methods and a smoothing property of the Schrödinger evolution group
cites work: SOME EXAMPLES OF SMOOTH OPERATORS AND THE ASSOCIATED SMOOTHING EFFECT
cites work: Small solutions to nonlinear Schrödinger equations
cites work: Asymptotic behavior at infinity for Green's functions of first order systems with characteristics of nonuniform multiplicity
cites work: Local regularity of solutions to wave equations with time-dependent potentials
cites work: Q3251547
cites work: Weighted Hardy spaces
cites work: A resolvent estimate and a smoothing property of inhomogeneous Schrödinger equations
description: scientific article; zbMATH DE number 1274829