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      Triplets of closely embedded Dirichlet type spaces on the unit polydisc

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      Author
      Cojuhari, P.
      Gheondea, A.
      Date
      2013
      Source Title
      Complex Analysis and Operator Theory
      Print ISSN
      1661-8254
      Electronic ISSN
      1661-8262
      Publisher
      Birkhaeuser Science
      Volume
      7
      Issue
      5
      Pages
      1525 - 1544
      Language
      English
      Type
      Article
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      Abstract
      We propose a general concept of triplet of Hilbert spaces with closed embeddings, instead of continuous ones, and we show how rather general weighted L2 spaces yield this kind of generalized triplets of Hilbert spaces for which the underlying spaces and operators can be explicitly calculated. Then we show that generalized triplets of Hilbert spaces with closed embeddings can be naturally associated to any pair of Dirichlet type spaces Dα(DN) of holomorphic functions on the unit polydisc DN and we explicitly calculate the associated operators in terms of reproducing kernels and radial derivative operators. We also point out a rigging of the Hardy space H2(DN) through a scale of Dirichlet type spaces and Bergman type spaces. © 2012 Springer Basel.
      Keywords
      Closed embedding
      Dirichlet type space on the unit polydisc
      Hamiltonian
      Kernel operator
      Rigged Hilbert spaces
      Triplet of Hilbert spaces
      Permalink
      http://hdl.handle.net/11693/20784
      Published Version (Please cite this version)
      http://dx.doi.org/10.1007/s11785-012-0269-z
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