Rudin’s orthogonality problem and the Nevanlinna counting function
Rudin’s orthogonality problem and the Nevanlinna counting function
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Rudin 的正交问题和 Nevanlinna 计数函数
DOI：
10.1090/s0002-9939-97-03694-0
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
P. Bourdon
中科院分区：
文献类型：
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作者：
P. Bourdon
设4是一个取开放单元磁盘U的全纯函数。我们证明了4的非负幂集在L2 （qU）中是正交的，当且仅当q的Nevanlinna计数函数是径向的。作为推论，我们得到{q': n = 0,1,2，…的正交性}对于一个单值0意味着对于某个常数ar +(z) = az。我们也证明了如果{nfl: n = 0,1,2，…}是正交的，那么+(U)的闭包一定是一个圆盘。
Let 4 be a holomorphic function taking the open unit disk U into itself. We show that the set of nonnegative powers of 4 is orthogonal in L2 (qU) if and only if the Nevanlinna counting function of q, No, is essentially radial. As a corollary, we obtain that the orthogonality of {q': n = 0, 1, 2,... } for a univalent 0 implies +(z) = az for some constant ar. We also show that if {nfl: n = 0, 1, 2, ... } is orthogonal, then the closure of +(U) must be a disk.