Matrix method for solving linear complex vector functional equations
type: Item
instance of: scholarly article
title: Matrix method for solving linear complex vector functional equations
zbMATH Open document ID: 1002.39034
DOI: 10.1155/S016117120200501X
author: Ice Risteski
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2002-08-13T00:00:00Z
full work available at URL: https://eudml.org/doc/49637
full work available at URL: S016117120200501X.html
review text: Let \(\mathcal V\) be a finite-dimensional complex vector space and let \(f:\mathcal V^n \to \mathcal V\); denote with \(\mathbb{Z}_i\) (\(1\leq i\leq n\)) the vectors in \(\mathcal V\). The main result gives the representation of the general solution of the cyclic non-homogeneous functional equation \[ \sum_{i=1}^n a_if(\mathbb{Z}_i, \mathbb{Z}_{i+1},\cdots,\mathbb{Z}_{i+n-1})=g(\mathbb{Z}_1,\mathbb{Z}_2,\cdots,\mathbb{Z}_n) \quad (\mathbb{Z}_{n+i}=\mathbb{Z}_i) \] where \(a_i\) are complex constants. The method developed is used for solving some other similar equations.
Mathematics Subject Classification ID: 39B32
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 1780335
zbMATH Keywords: matrix method
zbMATH Keywords: linear complex vector functional equation
zbMATH Keywords: complex vector space
reviewed by: Gian Luigi Forti
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1780335