Growth of Biregular Functions in Balls

Dirac算子零化的Clifford值函数称为正则函数，正则函数是全纯函数在高维空间中非交换领域的推广。双正则函数是双变量的正则函数。正则函数的增长性问题是Clifford分析中的重要问题之一。本文研究单位球上双正则函数的增长性问题。借鉴Wiman-Valiron理论，利用双正则函数的Taylor级数，研究双正则函数的增长阶，得到广义Lindelöf-Pringsheim定理，建立增长阶与Taylor级数的联系。The Clifford-valued functions of null-solutions of Dirac operator are called regular functions. A regular function is an extension of holomorphic functions in non-commutative domains in high-dimensional spaces. Biregular functions are regular functions of two variables. The growth problem of regular functions is one of the important problems in Clifford analysis. In this paper, we investigate the growth problem of biregular functions in unit balls. Drawing on Wiman-Valiron theory, the growth order of biregular functions is studied by using the Taylor series of biregular functions, and the generalization of Lindelöf-Pringsheim theorem is obtained. This theorem shows the relation between the growth order of biregular functions and the Taylor series.