Linear functional equations on the line
type: Item
instance of: scholarly article
title: Linear functional equations on the line
zbMATH Open document ID: 0824.39008
DOI: 10.1007/BF01203094
author: Victor M. Nicolaevsky
author: G. Belitskii
published in: Integral Equations and Operator Theory
publication date: 1995-11-14T00:00:00Z
review text: The functional equation \(\sum^ L_{j= 1} A_ j(x) y(F_ j x)= \gamma(x)\), where \(A_ j: \mathbb{R}\to \text{Hom}(\mathbb{C}^ m, \mathbb{C}^ n)\) and \(\gamma: \mathbb{R}\to \mathbb{C}^ n\) are given \(C^ k\)-maps and \(F_ j: \mathbb{R}\to \mathbb{R}\) are given \(C^ k\)-diffeomorphisms, is considered. A general theory of this equation via dynamical properties of the system \(\{F_ j\}\) is built. Results on the reduction of the global \(C^ k\)- solvability problem to the local one are given.
Mathematics Subject Classification ID: 39B42
Mathematics Subject Classification ID: 39B32
zbMATH DE Number: 764054
zbMATH Keywords: linear functional equations
zbMATH Keywords: diffeomorphisms
zbMATH Keywords: reduction
zbMATH Keywords: global solvability problem
reviewed by: Kazimierz Nikodem
MaRDI profile type: Publication
cites work: Q5592596
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description: scientific article; zbMATH DE number 764054