Orthogonal Gyroexpansion in Möbius Gyrovector Spaces. (13th December 2017)

• Record Type: Journal Article
• Authors: Watanabe, Keiichi
• Other Names: Martinez-Moreno Juan Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2017(2017)
• Publication Date: 2017-12-13
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2017/1518254
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : 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.