四元数空间中的正则逆紧映射

Proper slice regular functions over quaternions

全纯逆紧映射的研究是多复变函数论中一个重要且非常活跃的课题.本文研究四元数空间中的逆紧映射.特别地,对于四元数切片正则函数,本文利用其Hardy空间的分解定理证明四元数单位球上的自逆紧映射正是有限Blaschke乘积.此外,本文确定了此函数类中4维球壳上的自逆紧映射.

The study of proper holomorphic mappings is an important and very active topic in several complex variables.In this paper,we investigate the proper mapping in the quaternionic setting.In particular,the proper self-mappings of the open unit ball of quaternions are precisely finite Blaschke products by a factorization of Hardy spaces for quaternionic slice regular functions.In addition,the proper self-mappings of the four-dimensional spherical shell are determined for quaternionic slice regular functions.