On the quaternionic Monge-Ampere operator, closed positive currents and Lelong-Jensen type formula on the quaternionic space
On the quaternionic Monge-Ampere operator, closed positive currents and Lelong-Jensen type formula on the quaternionic space
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四元数Monge-Ampere算子、闭正电流和四元数空间上的Lelong-Jensen型公式
DOI：
10.1016/j.bulsci.2015.03.001
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发表时间：
2017
影响因子：
1.3
通讯作者：
Wang Wei
中科院分区：
文献类型：
--
作者：
Wan Dongrui;Wang Wei
本文在平坦的四元数空间Hn上引入了作用于四元数微分形式的一阶微分算子d 0和d1. d 0，d1和△= d 0 d1的行为与多复变函数中的ε，ε ε和ε的行为非常相似.四元数Monge-Ampère运算符可以定义为（△ u）n，并且有一个简单的显式表达式。我们在四元数情形下定义了闭合正电流的概念，并将复多能理论中的几个结果推广到四元数情形：定义了闭合正电流的Lelong数，得到了Lelong-Jensen型公式的四元数形式，推广了Bedford-Taylor理论，即将四元数Monge-Ampère算子的定义推广到局部有界的四元数多重次调和函数，并证明了相应的收敛定理.
In this paper, we introduce the first-order differential operators d 0 and d 1 acting on the quaternionic version of differential forms on the flat quaternionic space H n. The behavior of d 0, d 1 and△= d 0 d 1 is very similar to∂,∂‾ and∂∂‾ in several complex variables. The quaternionic Monge–Ampère operator can be defined as (△ u) n and has a simple explicit expression. We define the notion of a closed positive current in the quaternionic case, and extend several results in complex pluripotential theory to the quaternionic case: define the Lelong number of a closed positive current, obtain the quaternionic version of Lelong–Jensen type formula, and generalize Bedford–Taylor theory, ie, extend the definition of the quaternionic Monge–Ampère operator to locally bounded quaternionic plurisubharmonic functions and prove the corresponding convergence theorem.