Riesz和绿色能源在投影空间

A. Anderson, M. Dostert, P. Grabner, Ryan Matzke, T. Stepaniuk
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引用次数: 4

摘要

本文研究两点齐次空间上的Riesz、Green和对数能量。更准确地说,我们考虑实数、复数、四元数和Cayley投影空间。对于这些空间中的每一个,我们使用行列式点过程提供了上述能量的上限估计。此外,我们确定了这些相同数量级的能量的下界。
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Riesz and Green energy on projective spaces
In this paper we study Riesz, Green and logarithmic energy on two-point homogeneous spaces. More precisely we consider the real, the complex, the quaternionic and the Cayley projective spaces. For each of these spaces we provide upper estimates for the mentioned energies using determinantal point processes. Moreover, we determine lower bounds for these energies of the same order of magnitude.
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