论文标题
向后移位和Fock型空间的几乎不变子空间
Backward shift and nearly invariant subspaces of Fock-type spaces
论文作者
论文摘要
我们研究了加权Fock型空间$ \ MATHCAL {f} _W^p $中的向后移动不变和几乎不变子空间的结构，其权重$ w $不一定是径向。 We show that in the spaces $\mathcal{F}_W^p$ which contain the polynomials as a dense subspace (in particular, in the radial case) all nontrivial backward shift invariant subspaces are of the form $\mathcal{P}_n$, i.e., finite dimensional subspaces consisting of polynomials of degree at most $n$.通常，几乎不变子空间的结构更为复杂。在缓慢生长的空间（高度指数类型）的情况下，我们建立了De Branges订购定理的类似物。然后，我们构建了示例，这些示例表明，对于更大生长的一般Fock型空间，结果失败了。
We study the structure of the backward shift invariant and nearly invariant subspaces in weighted Fock-type spaces $\mathcal{F}_W^p$, whose weight $W$ is not necessarily radial. We show that in the spaces $\mathcal{F}_W^p$ which contain the polynomials as a dense subspace (in particular, in the radial case) all nontrivial backward shift invariant subspaces are of the form $\mathcal{P}_n$, i.e., finite dimensional subspaces consisting of polynomials of degree at most $n$. In general, the structure of the nearly invariant subspaces is more complicated. In the case of spaces of slow growth (up to zero exponential type) we establish an analogue of de Branges' Ordering Theorem. We then construct examples which show that the result fails for general Fock-type spaces of larger growth.
