全纯函数的模表征

H. Boche **, V. Pohl
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引用次数: 8

摘要

在(Boche, H. and Pohl, V., 2005),《磁盘代数中的谱分解》中得到了证明。复杂的变量。理论与应用,50,383-387 .),如果函数的模f在单位圆盘的闭包中是连续的,则函数f本身在那里一般不必是连续的。本文证明了如果一个函数的连续模是弱正则主量,则该模的连续性总是隐含着函数本身的连续性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Characterization of holomorphic functions in terms of their moduli
It was shown in (Boche, H. and Pohl, V., 2005, Spectral factorization in the disk algebra. Complex Variables. Theory and Applications, 50, 383–387.) that if the modulus |f| of a function is continuous in the closure of the unit disk, the function f itself needs not to be continuous there, in general. This article shows that if the modulus of continuity of a function is a weak regular majorant, the continuity of the modulus always implies the continuity of the function itself.
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