Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functions
Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functions
复制标题
全纯函数加权空间中采样和插值的严格密度不等式
DOI：
10.1016/j.jfa.2019.108282
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发表时间：
2018
影响因子：
1.7
通讯作者：
Jose Luis Romero
中科院分区：
文献类型：
--
作者：
K. Grōchenig;Antti Haimi;J. Ortega;Jose Luis Romero
在Lindholm问题的基础上，我们证明了多复变量整函数在多重次调和权下的Fock空间中的采样和插值的严格密度不等式.特别是，这些空间不允许同时采样和插值的集合。为了证明密度条件的最优性，我们构造了密度任意接近临界密度的采样集。该技术结合了联合收割机的方法，从几个复变量（估计）和一般再生核希尔伯特空间的局部框架的理论（没有解析性假设）。Fekete点和框架变形的抽象结果可能是独立的利益。
Answering a question of Lindholm, we prove strict density inequalities for sampling and interpolation in Fock spaces of entire functions in several complex variables defined by a plurisubharmonic weight. In particular, these spaces do not admit a set that is simultaneously sampling and interpolating. To prove optimality of the density conditions, we construct sampling sets with a density arbitrarily close to the critical density. The techniques combine methods from several complex variables (estimates for∂¯) and the theory of localized frames in general reproducing kernel Hilbert spaces (with no analyticity assumed). The abstract results on Fekete points and deformation of frames may be of independent interest.