A Carathéodory theorem for the bidisk via Hilbert space methods
A Carathéodory theorem for the bidisk via Hilbert space methods
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DOI：
10.1007/s00208-011-0650-7
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发表时间：
2010-02
影响因子：
1.4
通讯作者：
J. Agler;John E. McCarthy;N. Young
中科院分区：
文献类型：
--
作者：
J. Agler;John E. McCarthy;N. Young
如果φ是双圆盘上以1为界的解析函数，且是φ具有角梯度的点，则λ →τ在。这是一个模拟的bidisk的经典定理Carathéodory的磁盘。对于上述的φ，如果使得λ →τ的lim inf是有限的，则方向导数D −δφ（τ）对所有适当的方向都存在。此外，可以将φ和τ与Pick类中的解析函数相关联，使得方向导数的值可以用h表示。
Ifφis an analytic function bounded by 1 on the bidiskandis a point at whichφhas an angular gradientthenas λ →τnontangentially in. This is an analog for the bidisk of a classical theorem of Carathéodory for the disk. Forφas above, ifis such that the lim inf ofas λ →τis finite then the directional derivativeD−δφ(τ) exists for all appropriate directions. Moreover, one can associate withφandτan analytic functionhin the Pick class such that the value of the directional derivative can be expressed in terms ofh.