Beurling’s phenomenon on analytic Hilbert spaces over the complex plane
Beurling’s phenomenon on analytic Hilbert spaces over the complex plane
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DOI：
10.1090/s0002-9939-09-10196-x
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发表时间：
2010-04
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影响因子：
--
通讯作者：
Shuyun Wei
中科院分区：
文献类型：
--
作者：
Shuyun Wei
本文证明了复平面上解析Hilbert空间中类似于哈代空间或Bergman空间的Beurling定理不成立，但对于有限余维拟不变子空间，它们由游荡子空间生成当且仅当它们由zn生成，条件是再生核K λ（z）的阶小于2但不等于1.
In this paper, we show that Beurling's theorem on analytic Hilbert spaces over the complex plane analogous to the Hardy space or the Bergman space does not hold, but for finite co-dimensional quasi-invariant subspaces, they are generated by their wandering subspace if and only if they are generated by z n provided that the order of the reproducing kernels K λ (z) is less than 2 but not equal to 1.