Cyclicity of reproducing kernels in weighted Hardy spaces over the bidisk

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• 作者：Kou Hei Izuchi ^{izuchi@yamaguchi-u.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 47A15 ; 32A35 ; secondary ; 46E22 ; 47A16
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：272
• 期：2
• 页码：546-558
• 全文大小：289 K

文摘

In general, the Beurling theorem does not hold for an invariant subspace in the Hardy space over the bidisk. In 1991, Nakazi posed a conjecture that the Beurling theorem holds for a singly generated invariant subspace. In this paper, a relation between a singly generated invariant subspace and a weighted Hardy space over the bidisk is studied. It is showed that there exists a weighted Hardy space over the bidisk which has a non-cyclic reproducing kernel. Also a counterexample for Nakazi's conjecture is given.