摘要
本文综述了多四元变量的k-Cauchy-Fueter算子的研究进展,讨论了k-Cauchy-Fueter复形、非齐次k-Cauchy-Fueter方程、Hartogs扩张现象、Bochner-Martinelli积分表示公式、Penrose积分变换和k正则函数的级数展开、四元Hardy空间与Cauchy-Szeg¨o核、0-Cauchy-Fueter算子及与四元Monge-Amp`ere算子的关系、四元闭正流及其Lelong数、Lelong-Jessen型公式,以及切向k-CauchyFueter算子与复形.
This is a survey of the development of k-Cauchy-Fueter operators. We discuss the k-Cauchy-Fueter complexes, non-homogeneous k-Cauchy-Fueter equations, the Hartogs＇ extension phenomenon for k-regular functions, Bochner-Martinelli integral representation formula, Penrose integral transformation and series expansion of k-regular functions, quaternionic Hardy space and Cauchy-Szeg¨o kernel, the relation between 0-Cauchy-Fueter operator and quaternionic Monge-Ampere operator, quaternionic closed positive currents and their Lelong number,Lelong-Jessen type formula, and tangential k-Cauchy-Fueter operators and complexes.
出处
《中国科学：数学》
CSCD
北大核心
2015年第11期1791-1810,共20页
Scientia Sinica：Mathematica
基金
国家自然科学基金(批准号:11171298)资助项目
