Orthogonal gyroexpansion in Möbius gyrovector spaces
type: Item
instance of: scholarly article
title: Orthogonal gyroexpansion in Möbius gyrovector spaces
zbMATH Open document ID: 1391.46032
DOI: 10.1155/2017/1518254
author: Keiichi Watanabe
published in: Journal of Function Spaces
publication date: 2018-01-12T00:00:00Z
review text: Summary: We investigate the Möbius gyrovector spaces which are open balls centered at the origin in a real Hilbert space with the Möbius addition, the Möbius scalar multiplication, and the Poincaré metric introduced by Ungar. In particular, for an arbitrary point, we can easily obtain the unique closest point in any closed gyrovector subspace, by using the ordinary orthogonal decomposition. Further, we show that each element has the orthogonal gyroexpansion with respect to any orthogonal basis in a Möbius gyrovector space, which is similar to each element in a Hilbert space having the orthogonal expansion with respect to any orthonormal basis. Moreover, we present a concrete procedure to calculate the gyrocoefficients of the orthogonal gyroexpansion.
Mathematics Subject Classification ID: 46C99
zbMATH DE Number: 6825471
zbMATH Keywords: Möbius gyrovector spaces
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/1518254
OpenAlex ID: W2773822870
cites work: Extension of the unit disk gyrogroup into the unit ball of any real inner product space
cites work: Group-like structure underlying the unit ball in real inner product spaces
cites work: Q5433130
cites work: Q5715578
cites work: On a characterization of commutativity for {\(C^*\)}-algebras via gyrogroup operations
cites work: Generalized gyrovector spaces and a Mazur--Ulam theorem
cites work: Finitely generated gyrovector subspaces and orthogonal gyrodecomposition in the Möbius gyrovector space
cites work: Examples and applications of generalized gyrovector spaces
cites work: A confirmation by hand calculation that the Möbius ball is a gyrovector space
cites work: Q3322631
cites work: Convex analysis and optimization in Hadamard spaces
description: scientific article; zbMATH DE number 6825471