Unbounded Multipliers of Complete Pick Spaces

We examine densely defined (but possibly unbounded) multiplication operators in Hilbert function spaces possessing a complete Nevanlinna–Pick (CNP) kernel. For such a densely defined operator T , the domains of T and T ∗ are reproducing kernel Hilbert spaces contractively contained in the ambient sp...

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Bibliographic Details
Published in:Integral equations and operator theory 2022-06, Vol.94 (2), Article 14
Main Authors: Jury, Michael T., Martin, Robert T. W.
Format: Article
Language:English
Subjects:
Analysis
Domains
Function space
Hilbert space
Kernels
Mathematics
Mathematics and Statistics
Multiplication
Operators (mathematics)
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Summary:We examine densely defined (but possibly unbounded) multiplication operators in Hilbert function spaces possessing a complete Nevanlinna–Pick (CNP) kernel. For such a densely defined operator T , the domains of T and T ∗ are reproducing kernel Hilbert spaces contractively contained in the ambient space. We study several aspects of these spaces, especially the domain of T ∗ , which can be viewed as analogs of the classical deBranges–Rovnyak spaces in the unit disk.
ISSN:0378-620X
1420-8989
DOI:10.1007/s00020-022-02690-8