Padé算子连续的条件

On the Conditions for the Continuity of the Padé Operator

中文摘要:

      

英文摘要:

      Let r_{m, n}=P_{m, n}/ Q_{m, n} be the Padé approximation of order (m, n) for a given power series f: Q_{m, n}f- P_{m, n}= O(z^m+n+1+j), j is as large as possible, m′ ,n′ are the exact degree of p_{m, n} and Q_{m, n} respectively and d = min{m-m′ ,n-n′}. Let T_{m, n} be the operator that maps f on r_{m, n} . Then T_{m, n} is continuous if and only if d + (j-|j|)/2= 0. This condition is equal to that r_{m, n} is on the border of a Padé block.The results obtained by H. Werner and L.Wuytack have been modified and cor reeled in this paper.