：Beurling Type Theorem on the Hilbert Space Generated by a Positive Sequence论文

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作者（2019）在《Beurling Type Theorem on the Hilbert Space Generated by a Positive Sequence》一文中研究指出：Let H~2(γ) be the Hilbert space over the bidisk D~2 generated by a positive sequence γ ={γnm}n,m≥0. In this paper, we prove that the Beurling type theorem holds for the shift operator on H~2(γ) with γ = {γnm}n,m≥0 satisfying certain series of inequalities. As a corollary, we give several applications to a class of classical analytic reproducing kernel Hilbert spaces over the bidisk D~2.

Abstract

Let H~2(γ) be the Hilbert space over the bidisk D~2 generated by a positive sequence γ ={γnm}n,m≥0. In this paper, we prove that the Beurling type theorem holds for the shift operator on H~2(γ) with γ = {γnm}n,m≥0 satisfying certain series of inequalities. As a corollary, we give several applications to a class of classical analytic reproducing kernel Hilbert spaces over the bidisk D~2.

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