SwePub - sökning: id:"swepub:oai:lup.lub.lu.se:4...

Numrering	Referens	Omslagsbild	Hitta
1.	Aleman, Alexandru, et al. (författare) Weak products of complete pick spaces 2021 Ingår i: Indiana University Mathematics Journal. - : Indiana University Mathematics Journal. - 0022-2518. ; 70:1, s. 325-352 Tidskriftsartikel (refereegranskat)abstract 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.

Aleman, Alexandru, et al. (författare)
Weak products of complete pick spaces
2021
Ingår i: Indiana University Mathematics Journal. - : Indiana University Mathematics Journal. - 0022-2518. ; 70:1, s. 325-352
Tidskriftsartikel (refereegranskat)abstract
- 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.

Träfflista för sökning "id:"swepub:oai:lup.lub.lu.se:45680e52-b37a-4f4d-82b3-a36b3cc20960" "