The Patterson–Sullivan Reconstruction of Pluriharmonic Functions for Determinantal Point Processes on Complex Hyperbolic Spaces
The Patterson–Sullivan Reconstruction of Pluriharmonic Functions for Determinantal Point Processes on Complex Hyperbolic Spaces
复制标题
复双曲空间行列式点过程的多调和函数的帕特森-沙利文重构
DOI：
10.1007/s00039-022-00592-w
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发表时间：
2022
影响因子：
2.2
通讯作者：
Yanqi Qiu
中科院分区：
文献类型：
--
作者：
A. Bufetov;Yanqi Qiu
证明了Patterson-Sullivan重构几乎必然从Bergman函数在单位球上的Bergman核诱导的行列式点过程采样的随机离散子集上的值恢复Bergman函数。对于超临界加权Bergman空间，当函数在加权Bergman空间的单位球上时，重构是一致的。得到了任意维复双曲空间中固定重调和函数重构的充要条件，证明了加权Bergman空间的同时一致重构和加权调和哈代空间的强同时一致重构，并建立了Bergman空间一致同时重构的不可能性.
The Patterson–Sullivan reconstruction is proved almost surely to recover a Bergman function from its values on a random discrete subset sampled with the determinantal point process induced by the Bergman kernel on the unit ballin. For supercritical weighted Bergman spaces, the reconstruction is uniform when the functions range over the unit ball of the weighted Bergman space. We obtain a necessary and sufficient condition for reconstruction of a fixed pluriharmonic function in the complex hyperbolic space of arbitrary dimension; prove simultaneous uniform reconstruction for weighted Bergman spaces as well as strong simultaneous uniform reconstruction for weighted harmonic Hardy spaces; and establish the impossibility of the uniform simultaneous reconstruction for the Bergman spaceon.