2017年
Orthogonal Gyroexpansion in Möbius Gyrovector Spaces
Journal of Function Spaces
- 巻
- 2017
- 号
- 開始ページ
- 1
- 終了ページ
- 13
- 記述言語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1155/2017/1518254
- 出版者・発行元
- Hindawi Limited
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.
- リンク情報
- ID情報
-
- DOI : 10.1155/2017/1518254
- ISSN : 2314-8896
- eISSN : 2314-8888