The Fock space as a de Branges-Rovnyak space. (English) Zbl 1443.46017
Summary: 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.
MSC:
| 46E22 | Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) |
| 47A57 | Linear operator methods in interpolation, moment and extension problems |
| 30H45 | de Branges-Rovnyak spaces |
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