Orthogonal Gyroexpansion in Möbius Gyrovector Spaces

  title={Orthogonal Gyroexpansion in M{\"o}bius Gyrovector Spaces},
  author={Keiichi Watanabe},
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 M… CONTINUE READING

From This Paper

Topics from this paper.


Publications citing this paper.


Publications referenced by this paper.

Uniform Convexity, Hyperbolic Geometry and Nonexpansive Mappings, vol. 83 of Monographs and Textbooks in Pure and Applied Mathematics

  • K. Goebel, S. Reich
  • 1984
Highly Influential
5 Excerpts

Examples and applications of generalized gyrovector spaces

  • O.Hatori
  • Results inMathematics, vol. 71, no. 1-2, pp. 295…
  • 2017

Finitely generated gyrovector subspaces and orthogonal gyrodecomposition in the Möbius gyrovector space

  • T. Abe, K. Watanabe
  • Journal of Mathematical Analysis and Applications…
  • 2017
1 Excerpt

A confirmation by hand calculation that the Möbius ball is a gyrovector space

  • K. Watanabe
  • Nihonkai Mathematical Journal, vol. 27, no. 1-2…
  • 2016

Generalized gyrovector spaces and a Mazur-Ulam theorem

  • T. Abe, O. Hatori
  • Publicationes Mathematicae Debrecen, vol. 87, no…
  • 2015

Analytic hyperbolic geometry and Albert Einstein’s special theory of relativity

  • A. A. Ungar
  • World Scientific Publishing Co. Pte. Ltd., Toh…
  • 2008
3 Excerpts

Analytic Hyperbolic Geometry, World Scientific Publishing Co

  • A. A. Ungar
  • Pte. Ltd., Hackensack, NJ,
  • 2005
1 Excerpt

Extension of the unit disk gyrogroup into the unit ball of any real inner product space

  • A. A. Ungar
  • Journal of Mathematical Analysis and Applications…
  • 1996

Group-like structure underlying the unit ball in real inner product spaces

  • A. A. Ungar
  • Results in Mathematics, vol. 18, no. 3-4, pp. 355…
  • 1990

Similar Papers

Loading similar papers…