Clifford连分式的值域与元素域(英文)

Value regions and element regions of Clifford continued fractions

首先将复连分式的值域与元素域的概念推广到了Clifford连分式,得到了Clifford连分式值域与元素域的两条性质;其次构造出了一对满足条件的值域与元素域序列,并由所构造出来的值域与元素域的一个特殊形式,将复连分式的区域套定理推广到了Clifford连分式的更一般的情形;最后由Clifford连分式值域与元素域的性质和所构造出的一对满足条件的值域与元素域序列,得到了收敛的Clifford连分式。

Firstly, the concepts of value regions and element regions of complex continued fractions are generalized to the case of Clifford continued fractions, and thereby two properties of Clifford continued fractions are obtained. Secondly, a pair of the sequences of value regions and element regions are con- structed, and the nested region theorem in Clifford continued fractions is established by using the special case of the constructed sequences. In the end, some convergent Clifford continued fractions are obtained by using the obtained properties and the constructed sequences about the Clifford continued fractions.