Abstract

We examine a way of using the parametric continuation method to compute mappings of the unit ball in \(n\)-dimensional real space. The proposed approach yielded sufficient and necessary conditions for the global injectivity of mappings were obtained. It is established that these conditions actually coincide with the known features of the \(n\)-dimensional complex space. The concretization of the method made here are the generalizations of some classes of functions analytic in the unit circle. In addition, the analogue of the Kaplan class was derived for mappings in \(n\)-dimensional real space.

中文翻译：

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关于$$ \ boldsymbol {R} ^ {\ boldsymbol {n}} $$中的参数连续方法

摘要

我们研究了一种使用参数连续方法来计算单位球在\（n \）维实空间中的映射的方法。所提出的方法为映射的全局注入性提供了充分和必要的条件。可以确定的是，这些条件实际上与\（n \）维复空间的已知特征一致。这里进行的方法的具体化是单位圆中分析的某些类函数的推广。另外，派生Kaplan类的类似物用于\（n \）维实空间中的映射。