On an abstract analog of the Krylov-Bogolyubov transformation in the theory of perturbations of linear operators
type: Item
instance of: scholarly article
title: On an abstract analog of the Krylov-Bogolyubov transformation in the theory of perturbations of linear operators
zbMATH Open document ID: 0962.47030
DOI: 10.1007/BF02465196
publication date: 2001-06-04T00:00:00Z
review text: The paper deals with the family of operators \(L=A+\varepsilon F\), where \(A\) is a closed densely defined linear operator in a Banach space \(X\), \(F\) is a nonlinear map in \(X\) which satisfies a Lipschitz-type condition and \(\varepsilon\) is a small parameter. The authors describes an abstract analogue of the Krylov-Bogolyubov transformation for the ``perturbed'' operator \(L\) and studies some properties of such a transformation. The paper contains no proofs.
reviewed by: V. A. Liskevich
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 34C29
zbMATH DE Number: 1407630
zbMATH Keywords: Krylov-Bogolyubov transformation
zbMATH Keywords: averaging method
author: Anatoly G. Baskakov
MaRDI profile type: Publication
cites work: Q5641407
cites work: Q5517170
cites work: SPECTRAL ANALYSIS OF PERTURBED NONQUASIANALYTIC AND SPECTRAL OPERATORS
cites work: Q5654646
cites work: Krylov-Bogolyubov substitution in the perturbation theory of linear operators
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 1407630