Additive invariants on the Hardy space over the polydisc

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In recent years various advances have been made with respect to the Nevanlinna-Pick kernels, especially on the symmetric Fock space, while the development on the Hardy space over the polydisc is relatively slow. In this paper, several results known on the symmetric Fock space are proved for the Hardy space over the polydisc. The known proofs on the symmetric Fock space make essential use of the Nevanlinna-Pick properties. Specifically, we study several integer-valued numerical invariants which are defined on an arbitrary invariant subspace of the vector-valued Hardy spaces over the polydisc. These invariants include the Samuel multiplicity, curvature, fiber dimension, and a few others. A tool used to overcome the difficulty associated with non-Nevanlinna-Pick kernels is Tauberian theory.

Original languageEnglish
Pages (from-to)359-372
Number of pages14
JournalJournal of Functional Analysis
Issue number1
StatePublished - 1 Dec 2007


  • Curvature
  • Defect operator
  • Fiber dimension
  • Hardy space, polydisc
  • Samuel multiplicity


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