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Orthogonal Gyroexpansion in Möbius Gyrovector Spaces
Author
Source
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-12-13
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Watanabe, Keiichi. 2017. Orthogonal Gyroexpansion in Möbius Gyrovector Spaces. Journal of Function Spaces،Vol. 2017, no. 2017, pp.1-13.
https://search.emarefa.net/detail/BIM-1176310
Modern Language Association (MLA)
Watanabe, Keiichi. Orthogonal Gyroexpansion in Möbius Gyrovector Spaces. Journal of Function Spaces No. 2017 (2017), pp.1-13.
https://search.emarefa.net/detail/BIM-1176310
American Medical Association (AMA)
Watanabe, Keiichi. Orthogonal Gyroexpansion in Möbius Gyrovector Spaces. Journal of Function Spaces. 2017. Vol. 2017, no. 2017, pp.1-13.
https://search.emarefa.net/detail/BIM-1176310
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1176310