Angular measures and Birkhoff orthogonality in Minkowski planes

Let x and y be two unit vectors in a normed plane [Formula: see text] . We say that x is Birkhoff orthogonal to y if the line through x in the direction y supports the unit disc. A B-measure (Fankhänel in Beitr Algebra Geom 52(2):335–342, 2011) is an angular measure [Formula: see text] on the unit c...

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Autores principales: Naszódi, Márton, Prokaj, Vilmos, Swanepoel, Konrad
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7474716/
https://www.ncbi.nlm.nih.gov/pubmed/32952199
http://dx.doi.org/10.1007/s00010-020-00715-4
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author Naszódi, Márton
Prokaj, Vilmos
Swanepoel, Konrad
author_facet Naszódi, Márton
Prokaj, Vilmos
Swanepoel, Konrad
author_sort Naszódi, Márton
collection PubMed
description Let x and y be two unit vectors in a normed plane [Formula: see text] . We say that x is Birkhoff orthogonal to y if the line through x in the direction y supports the unit disc. A B-measure (Fankhänel in Beitr Algebra Geom 52(2):335–342, 2011) is an angular measure [Formula: see text] on the unit circle for which [Formula: see text] whenever C is a shorter arc of the unit circle connecting two Birkhoff orthogonal points. We present a characterization of the normed planes that admit a B-measure.
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spelling pubmed-74747162020-09-16 Angular measures and Birkhoff orthogonality in Minkowski planes Naszódi, Márton Prokaj, Vilmos Swanepoel, Konrad Aequ Math Article Let x and y be two unit vectors in a normed plane [Formula: see text] . We say that x is Birkhoff orthogonal to y if the line through x in the direction y supports the unit disc. A B-measure (Fankhänel in Beitr Algebra Geom 52(2):335–342, 2011) is an angular measure [Formula: see text] on the unit circle for which [Formula: see text] whenever C is a shorter arc of the unit circle connecting two Birkhoff orthogonal points. We present a characterization of the normed planes that admit a B-measure. Springer International Publishing 2020-02-22 2020 /pmc/articles/PMC7474716/ /pubmed/32952199 http://dx.doi.org/10.1007/s00010-020-00715-4 Text en © The Author(s) 2020 Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Article
Naszódi, Márton
Prokaj, Vilmos
Swanepoel, Konrad
Angular measures and Birkhoff orthogonality in Minkowski planes
title Angular measures and Birkhoff orthogonality in Minkowski planes
title_full Angular measures and Birkhoff orthogonality in Minkowski planes
title_fullStr Angular measures and Birkhoff orthogonality in Minkowski planes
title_full_unstemmed Angular measures and Birkhoff orthogonality in Minkowski planes
title_short Angular measures and Birkhoff orthogonality in Minkowski planes
title_sort angular measures and birkhoff orthogonality in minkowski planes
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7474716/
https://www.ncbi.nlm.nih.gov/pubmed/32952199
http://dx.doi.org/10.1007/s00010-020-00715-4
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