Orthogonal Gyroexpansion in Möbius Gyrovector Spaces

@inproceedings{Watanabe2017OrthogonalGI,
  title={Orthogonal Gyroexpansion in M{\"o}bius Gyrovector Spaces},
  author={Keiichi Watanabe},
  year={2017}
}
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

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