Weak conditions for interpolation in holomorphic spaces
Weak conditions for interpolation in holomorphic spaces
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全纯空间插值的弱条件
DOI：
10.5565/publmat_44100_11
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发表时间：
2000
影响因子：
1.1
通讯作者：
K. Seip
中科院分区：
文献类型：
--
作者：
A. Schuster;K. Seip
一个类似于一致分离序列的概念，用极值函数表示，给出了在Lp空间中Paley-Wiener型全纯函数插值的一个充分必要条件，当$0 <p\leq 1$时，Fock型全纯函数插值，当$0 < p \leq 2$时，Bergman型全纯函数插值。此外，如果一个一致离散序列对于任何这样的Lp空间（$0 < p < \infty$）具有某种一致非唯一性，则它是该空间的插值序列。这些结果的证明是基于一个次调和函数的逼近定理，Beurling的结果关于序列的极限，和描述的插值序列的Beurling型密度。细节只进行了福克空间，这是最困难的情况。
An analogue of the notion of uniformly separated sequences, expressed in terms of extremal functions, yields a necessary and sufficient condition for interpolation in Lp spaces of holomorphic functions of Paley-Wiener-type when $0 < p \leq 1$, of Fock-type when $0 < p \leq 2$, and of Bergman-type when $0 < p < \infty$. Moreover, if a uniformly discrete sequence has a certain uniform non-uniqueness property with respect to any such Lp space ($0 < p < \infty$), then it is an interpolation sequence for that space. The proofs of these results are based on an approximation theorem for subharmonic functions, Beurling's results concerning compactwise limits of sequences, and the description of interpolation sequences in terms of Beurling-type densities. Details are carried out only for Fock spaces, which represent the most difficult case.