Realization of functions on the symmetrized bidisc
Realization of functions on the symmetrized bidisc
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DOI：
10.1016/j.jmaa.2017.04.003
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发表时间：
2017-04
影响因子：
1.3
通讯作者：
J. Agler;N. Young;N. Young
中科院分区：
文献类型：
--
作者：
J. Agler;N. Young;N. Young
我们证明了对称bidisc上模数为1的解析函数的实现公式和模型公式G= def {(z+ w, z w):| z|< 1,| w|< 1}。作为一个应用，我们证明了 Pick 型定理，给出了满足有限插值条件集的函数存在性的标准。
We prove a realization formula and a model formula for analytic functions with modulus bounded by 1 on the symmetrized bidisc G= def {(z+ w, z w):| z|< 1,| w|< 1}. As an application we prove a Pick-type theorem giving a criterion for the existence of such a function satisfying a finite set of interpolation conditions.