Orthogonality and additivity modulo \(\mathbb{Z}\)
type: Item
instance of: scholarly article
title: Orthogonality and additivity modulo \(\mathbb{Z}\)
zbMATH Open document ID: 0828.39010
DOI: 10.1007/BF03323038
author: Gian Luigi Forti
author: Karol Baron
published in: Results in Mathematics
publication date: 1996-01-11T00:00:00Z
review text: Suppose that \(E\) is a real topological vector space. If \(f: E\to \mathbb{R}\) satisfies (1) \(f(x+ y)- f(x)- f(y)\in \mathbb{Z}\) for all \(x,y\in E\) and if there exist a non-empty open set \(U\subset E\) and a \(\gamma\in (0, 1/2)\) such that \(f(U)\subset (- \gamma, \gamma)+ \mathbb{Z}\), then there exists a continuous linear functional \(g: E\to \mathbb{R}\) such that \(f(x)- g(x)\in \mathbb{Z}\) for every \(x\in E\). The authors prove an analogous result by assuming (1) for orthogonal \(x\), \(y\) from a real inner product space and they apply it for orthogonally exponential functions. For the earlier result see for example the first author and \textit{P. Volkmann} [Abh. Math. Semin. Univ. Hamb. 61, 189-195 (1991; Zbl 0753.39002)].
reviewed by: Themistocles M. Rassias
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 785160
zbMATH Keywords: orthogonality
zbMATH Keywords: additivity modulo \(\mathbb{Z}\)
zbMATH Keywords: topological vector space
zbMATH Keywords: inner product space
zbMATH Keywords: orthogonally exponential functions
MaRDI profile type: Publication
cites work: Q5289830
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description: scientific article; zbMATH DE number 785160