The periodic dilation completeness problem: cyclic vectors in the Hardy space over the infinite‐dimensional polydisk

DOI10.1112/jlms.12365zbMath1465.42039arXiv1908.03113OpenAlexW3040278112MaRDI QIDQ4991938

Kunyu Guo, Hui Dan

Publication date: 4 June 2021

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.03113

zbMATH Keywords

Bohr transformcyclic vectors in a Hardy space

Mathematics Subject Classification ID

Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Completeness of sets of functions in nontrigonometric harmonic analysis (42C30) Spaces of differentiable or holomorphic functions on infinite-dimensional spaces (46E50) Cyclic vectors, hypercyclic and chaotic operators (47A16)

Related Items (9)

Toeplitz operators on the Hardy space over the infinite-dimensional polydisc ⋮ Linear combinations of composition operators induced by linear fractional maps on the infinite polydisk ⋮ Integration operators on spaces of Dirichlet series ⋮ Power dilation systems {𝑓(𝑧^{𝑘})}_{𝑘∈ℕ} in Dirichlet-type spaces ⋮ Dilation theory and analytic model theory for doubly commuting sequences of \(C_{\cdot 0}\)-contractions ⋮ Helson operators and coinvariant subspaces ⋮ A weighted composition semigroup related to three open problems ⋮ Cyclic vectors, outer functions and Mahler measure in two variables ⋮ Splitting the Riesz basis condition for systems of dilated functions through Dirichlet series

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