Corresponding Banach spaces on time scales
type: Item
instance of: scholarly article
title: Corresponding Banach spaces on time scales
zbMATH Open document ID: 1074.39021
author: Andreas Ruffing
author: Moritz Simon
published in: Journal of Computational and Applied Mathematics
publication date: 2005-06-01T00:00:00Z
review text: Let \({\mathbb T}\) be a time scale, i.e. a nonempty closed subset of \({\mathbb R}\). The authors prove that for a given vector space \((\tilde V,+,\cdot)\) of functions \(f:{\mathbb T}\to{\mathbb R}\) and for the corresponding vector space \((V,\oplus,\odot)\) of positively regressive functions \(p\) (i.e., \(1+\mu(x)p(x)>0\) on \({\mathbb T}\) with the operations \(\oplus\) and \(\odot\) defined in ``usual'' time scales way), the cylinder transform \(\xi_\mu:(V,\oplus,\odot)\to(\tilde V,+,\cdot)\) is an isomorphism. This result is then extended to the Banach and Hilbert spaces setting.
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 39A13
zbMATH DE Number: 2173202
zbMATH Keywords: time scale
zbMATH Keywords: regressivity
zbMATH Keywords: cylinder transform
zbMATH Keywords: isometry
zbMATH Keywords: Banach and Hilbert spaces
reviewed by: Roman Šimon Hilscher
MaRDI profile type: Publication
full work available at URL: j.cam.2004.09.047
OpenAlex ID: W1995512402
cites work: Miscellaneous dynamic equations
cites work: Q2723195
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cites work: Square integrability of Gaussian bells on time scales
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DOI: 10.1016/J.CAM.2004.09.047
description: scientific article; zbMATH DE number 2173202