N[a,b]类中边界Nevanlinna-Pick插值(I)

The Boundary Nevanlinna-Pick Interpolation In the Class N[a,b]

中文关键词:  N[a  b]类  BNP（N[a  b]）问题  Hausdorff矩量问题  Hankel向量  角导数

英文关键词:N[a  b] class  BNP （N[a  b]） problem  Hausdorff moment problem  angle derivative.

中文摘要:

      用所谓的Hankel向量方法求解N[a,b]函数类中带边界插值数据的Nevanlina-Pick插值(BNP(N[a,b]))问题,并建立BNP(N[a,b])问题与[a,b]上的某种带约束条件的Hausdorff矩量问题之间等价的可解条件以及解之间明确的一一对应关系.这使得当BNP(N[a,b])问题有多解时,能通过带约束条件的矩量问题的可解性准则和解获得BNP(N[a,b])问题的可解性准则和解的参数化描述,而在唯一解的情况下,通过BNP(N[a,b])问题解的存在唯一性准则和唯一解来获得带约束条件的

英文摘要:

      We solve the BNP (N[a,b]) problem and establish one-to-one correspondence between the solutions to the BNP (N[a,b]) problem and the solutions to the Hausdorff mon-ment problem with a constrain by using the so-called Hankcl vector approach. This enables one to obtain the solvability criteria and the parametrized description of the BNP (N[a,b]) problem by those of the Hausdorff moment problem when there exist infinite solutions,and the situation is opposite when there exists exactly one solution.