多四元变量的k-Cauchy-Fueter算子  

The k-Cauchy-Fueter operators in several quaternionic variables

作　　者：王伟[1] 

机构地区：[1]浙江大学数学科学学院,杭州310027

出　　处：《中国科学：数学》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

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.

关 键 词：k-Cauchy-Fueter算子与复形 K正则函数 四元多重位势论 切向k-Cauchy-Fueter算子与复形 

分 类 号：O177[理学—数学]