Cyclicity of reproducing kernels in weighted Hardy spaces over the bidisk

被引：2

作者：

Izuchi, Kou Hei ^{[1
]}

机构：

[1] Yamaguchi Univ, Dept Math Educ, Yamaguchi 7538511, Japan

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2017年 / 272卷 / 02期

关键词：

Hardy space over the bidisk; Singly generated invariant subspaces; Reproducing kernels in weighted; Hardy spaces; INVARIANT SUBSPACES;

D O I：

10.1016/j.jfa.2016.09.025

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：546 / 558

页数：13

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