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Weak products of co...
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Aleman, AlexandruLund University,Lunds universitet,Matematik (naturvetenskapliga fakulteten),Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematics (Faculty of Sciences),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH
(författare)
Weak products of complete pick spaces
- Artikel/kapitelEngelska2021
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Indiana University Mathematics Journal,2021
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28 s.
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LIBRIS-ID:oai:lup.lub.lu.se:45680e52-b37a-4f4d-82b3-a36b3cc20960
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https://lup.lub.lu.se/record/45680e52-b37a-4f4d-82b3-a36b3cc20960URI
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https://doi.org/10.1512/iumj.2021.70.8122DOI
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Språk:engelska
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Sammanfattning på:engelska
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Let H be the Drury-Arveson or Dirichlet space of the unit ball of Cd. The weak product H ☉ H of H is the collection of all functions h that can be written as h =∑∞n=1 fngn, where ∑∞n=1 ||fn|| ||gn|| < ∞. We show that H ☉ H is contained in the Smirnov class of H; that is, every function in H ☉ H is a quotient of two multipliers of H, where the function in the denominator can be chosen to be cyclic in H . As a consequence, we show that the map N → closH ☉H N establishes a one-to-one and onto correspondence between the multiplier invariant subspaces of H and of H ☉ H . The results hold for many weighted Besov spaces H in the unit ball of Cd provided the reproducing kernel has the complete Pick property. One of our main technical lemmas states that, for weighted Besov spaces H that satisfy what we call the multiplier inclusion condition, any bounded column multiplication operator H → ⊕∞n=1 H induces a bounded row multiplication operator ⊕∞n=1 H → H . For the Drury-Arveson space Hd2 this leads to an alternate proof of the characterization of interpolating sequences in terms of weak separation and Carleson measure conditions.
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Hartz, MichaelWashington University in St. Louis
(författare)
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McCarthy, John E.Washington University in St. Louis
(författare)
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Richter, StefanUniversity of Tennessee
(författare)
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Matematik (naturvetenskapliga fakulteten)Matematikcentrum
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Ingår i:Indiana University Mathematics Journal: Indiana University Mathematics Journal70:1, s. 325-3520022-2518
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