【摘要】 <正> 1 引 言 称如下的连分式:为向量值连分式,这里a_i∈C,i=1,2,...,(?)_i∈C~d,i=0,1,2,.... 上述(1)的计算过程由Samelson逆确定,即更多还原

【Abstract】 The aim of this work is to give some criteria on the convergence of vector valued continued fractions defined by Samelson inverse. We give a new approach to prove the convergence theory of continued fractions. First, by means of the modified classical backward recurrence relation, we obtain a formula between the m-th and n-th convergence of vector valued continued fractions. Second, using this formula, we give necessary and sufficient conditions for the convergence of vector valued continued fractions.更多还原