Orthogonal Gyroexpansion in Mobius Gyrovector Spaces
Orthogonal Gyroexpansion in Mobius Gyrovector Spaces
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DOI：
10.1155/2017/1518254
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发表时间：
2017-01-01
影响因子：
1.9
通讯作者：
Watanabe, Keiichi
中科院分区：
文献类型：
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作者：
Watanabe, Keiichi
利用Mobius加法、Mobius标量乘法和Ungar引入的Poincare度规研究了实数Hilbert空间中以原点为中心的开球Mobius陀螺矢量空间。特别地，对于任意点，我们可以很容易地用普通正交分解得到任何封闭的陀螺矢量子空间中唯一的最近点。进一步，我们证明了每个元素对于莫比乌斯回旋矢量空间中的任何正交基都具有正交展开，这类似于希尔伯特空间中的每个元素对于任何正交基都具有正交展开。此外，我们还给出了正交回旋展开的回旋系数的具体计算方法。
We investigate the Mo bius gyrovector spaces which are open balls centered at the origin in a real Hilbert space with the Mobius addition, the Mobius scalar multiplication, and the Poincare 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 Mobius 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.