Positive resonances and the limiting amplitude principle
type: Item
instance of: scholarly article
title: Positive resonances and the limiting amplitude principle
zbMATH Open document ID: 0607.34003
DOI: 10.1007/BF00416462
author: B. George
published in: Letters in Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: Suppose that the Cauchy problem \[ d^ 2w/dt^ 2+Aw=e^{-iwt}f,\quad t>0,\quad w|_{t=0}=dw/dt|_{t=0}=0 \] (A is a positive selfadjoint operator in the separable Hilbert space H, \(w>0\), \(f\in H\), \(w: (0,t)\to H)\) has a unique solution and that conditions are satisfied in order that \(w=e^{-iwt}u+o(1)\), where u satisfies (3) \(\bar Au=e^{- iwt}u+f\). In the presence of resonance for \(\lambda\geq 0\), (3) may not be satisfied. The author gives a suitable definition for the positive resonance so that relations analogous to (3) remain valid.
reviewed by: Adolf Haimovici
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 47A50
zbMATH DE Number: 3981563
zbMATH Keywords: separable Hilbert space
MaRDI profile type: Publication
cites work: THE PRINCIPLE OF LIMIT AMPLITUDE
cites work: Asymptotic expansions in time for solutions of Schrödinger-type equations
cites work: Ein resonanzphänomen in der theorie akustischer und elektromagnetischer wellen
full work available at URL: https://doi.org/10.1007/bf00416462
OpenAlex ID: W1977026094
description: scientific article; zbMATH DE number 3981563