关于Drury-Arveson空间的一类平移不变子空间
On a class of shift-invariant subspaces of the Drury-Arveson space
AI总结：
本文研究Drury-Arveson空间中一类由满足$Y+e_j\subset Y$的集合$Y$定义的平移不变子空间，证明其可作为再生核Hilbert空间且核函数与相关Hankel算子符号均可显式计算，并指出该空间是Drury不等式最优适应到交换压缩算子子族的合适载体。
摘要：
在Drury-Arveson空间中，我们考虑其Taylor系数支撑在集合$Y\subset\mathbb{N}^d$的补集上的函数子空间，其中$Y$满足对所有$j=1,\dots,d$都有$Y+e_j\subset Y$。这是一个平移不变子空间的简单例子，它本身可以被视为一个再生核Hilbert空间（RKHS），其核函数可以被显式计算。此外，每一个这样的空间都可以看作Hankel算子的核的交集，这些Hankel算子的符号也可以被显式计算。最后，这是Drury不等式可以被最优地适应到Drury最初考虑的一族交换压缩算子的子族上的合适空间。
英文摘要：
In the Drury-Arveson space, we consider the subspace of functions whose Taylor coefficients are supported in the complement of a set $Y\subset\mathbb{N}^d$ with the property that $Y+e_j\subset Y$ for all $j=1,\dots,d$. This is an easy example of shift-invariant subspace, which can be considered as a RKHS in is own right, with a kernel that can be explicitely calculated. Moreover, every such a space can be seen as an intersection of kernels of Hankel operators, whose symbols can be explicity calcuated as well. Finally, this is the right space on which Drury's inequality can be optimally adapted to a sub-family of the commuting and contractive operators originally considered by Drury.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
