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The Fock Space as a De Branges–Rovnyak Space

  • Daniel AlpayEmail author
  • Fabrizio Colombo
  • Irene Sabadini
Article
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Abstract

We show that de Branges–Rovnyak spaces include as special cases a number of spaces, such as the Hardy space, the Fock space, the Hardy–Sobolev space and the Dirichlet space. We present a general framework in which all these spaces can be obtained by specializing a sequence that appears in the construction. We show how to exploit this approach to solve interpolation problems in the Fock space.

Keywords

De Branges–Rovnyak spaces Fock space Interpolation Reproducing kernel methods 

Mathematics Subject Classification

46E22 47A57 

Notes

Acknowledgements

The authors are grateful to the anonymous referee for pointing out reference [8].

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Daniel Alpay
    • 1
    Email author
  • Fabrizio Colombo
    • 2
  • Irene Sabadini
    • 2
  1. 1.Faculty of Mathematics, Physics, and Computation, Schmid College of Science and TechnologyChapman UniversityOrangeUSA
  2. 2.Dipartimento di MatematicaPolitecnico di MilanoMilanItaly

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