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- W3042245040 abstract "We provide a general framework to construct large vector spaces generated by bounded universal functions. We provide necessary and sufficient conditions on a sequence of automorphisms φn of a domain Ω in CN for there to exist a norm-closed infinite-dimensional vector space V generated by functions in B={f∈H∞(Ω)|‖f‖∞≤1} such that V is locally uniformly dense in H∞(Ω), V is linearly isometric with ℓ1, and every f∈V with ‖f‖=1 is universal for the composition operators Cφn:f↦f∘φn, by which we mean the set {f∘φn|n≥1} is locally uniformly dense in B. In the case when Ω is a bounded symmetric domain in CN, we provide sufficient conditions on a sequence of holomorphic self-maps φn of Ω for there to exist a vector space V generated by a locally uniformly dense set of inner functions such that V has each of the properties mentioned above." @default.
- W3042245040 created "2020-07-23" @default.
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- W3042245040 date "2020-12-01" @default.
- W3042245040 modified "2023-09-24" @default.
- W3042245040 title "Large vector spaces generated by bounded universal functions" @default.
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- W3042245040 doi "https://doi.org/10.1016/j.jmaa.2020.124393" @default.
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