Solutions to the operator equation \(i\varepsilon dy/dt=A(t)y\) on intervals containing turning points
type: Item
instance of: scholarly article
title: Solutions to the operator equation \(i\varepsilon dy/dt=A(t)y\) on intervals containing turning points
zbMATH Open document ID: 0964.34039
DOI: 10.1007/BF02551243
author: E. A. Grinina
published in: Theoretical and Mathematical Physics
publication date: 2000-11-23T00:00:00Z
review text: The author studies the asymptotic behavior as \(\varepsilon \rightarrow 0\) of the solution to the equation \[ i \varepsilon \frac{dy}{dt} =A(t)y , \] where \(A(t)\) is a linear closed operator defined on a dense subset of a Banach space \(X\). The solutions to the above equation are constructed as formal asymptotic expansions as \(\varepsilon \rightarrow 0\) on intervals containing parabolic or hyperbolic turning points. A recursive scheme for finding the succesive terms of these expansions are obtained.
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34E20
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 34E05
zbMATH DE Number: 1535336
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: parabolic turning points
zbMATH Keywords: hyperbolic turning points
zbMATH Keywords: spectrum of an operator
reviewed by: Narcisa Apreutesei
MaRDI profile type: Publication
cites work: Turning points for adiabatically perturbed periodic equations
cites work: Q5582545
cites work: Q3659207
description: scientific article; zbMATH DE number 1535336