Linear functional equations and their solutions in Lorentz spaces
type: Item
instance of: scholarly article
title: Linear functional equations and their solutions in Lorentz spaces
author: Janusz Morawiec
author: Thomas Zürcher
published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
publication date: 2022-06-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/2101.02428
review text: Assume that \(\Omega\subset\mathbb{R}^k\) is an open set, \(V\) is a (real or complex) separable Banach space, further \(f_1,\dots,f_N\colon\Omega\to\Omega\) and \(g_1,\dots,g_N\colon\Omega\to V\), \(h_0\colon\Omega\to V\) are given functions. The main result of the paper is an existence and uniqueness theorem for the solution \(\varphi\colon\Omega\to V\) of the linear functional equation \[ \varphi=\sum_{k=1}^N g_k\cdot(\varphi\circ f_k)+h_0 \] in Lorenz spaces. The approach is based on fixed point methods. In order to apply the Banach contraction principle, the change of variables formula by Hajłasz is needed.
reviewed by: Mihály Bessenyei
Mathematics Subject Classification ID: 47A50
Mathematics Subject Classification ID: 26A24
Mathematics Subject Classification ID: 39B12
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 7541285
zbMATH Keywords: linear operators
zbMATH Keywords: approximate differentiability
zbMATH Keywords: Luzin's condition \(N\)
zbMATH Keywords: functional equations
zbMATH Keywords: Lorentz spaces
MaRDI profile type: Publication
OpenAlex ID: W3119380492
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DOI: 10.1007/S13398-022-01259-9
description: scientific article; zbMATH DE number 7541285