论文标题
插值没有换向因素
Interpolation without commutants
论文作者
论文摘要
我们引入了一种“双空间方法”，以在磁盘上的Holomorthic函数的Banach空间X中混合Nevanlinna-Pick/Carathéodory-Schur插值。我们的方法可以看作是D. Sarason和B. Nagy-c.foiaş的众所周知的换向提升方法的补充。我们通过Hahn-Banach定理来计算X中X中最小的interpolant的规范，我们用来扩展在内核子空间上定义的函数而不增加其标准。这种功能扩展引理与Sarason的换向提升定理起着相似的作用，但仅涉及X的预期，不需要Hilbert空间结构。例如，我们介绍了beurling-sobolev空间的各个挑选型插值定理。
We introduce a "dual-space approach" to mixed Nevanlinna-Pick/Carathéodory-Schur interpolation in Banach spaces X of holomorphic functions on the disk. Our approach can be viewed as complementary to the well-known commutant lifting approach of D. Sarason and B. Nagy-C.Foiaş. We compute the norm of the minimal interpolant in X by a version of the Hahn-Banach theorem, which we use to extend functionals defined on a subspace of kernels without increasing their norm. This Functional extensions lemma plays a similar role as Sarason's Commutant lifting theorem but it only involves the predual of X and no Hilbert space structure is needed. As an example, we present the respective Pick-type interpolation theorems for Beurling-Sobolev spaces.
