Compressed resolvents of selfadjoint contractive exit space extensions and holomorphic operator-valued functions associated with them
DOI:
Keywords:
Selfadjoint extension, compressed resolvent, transfer functionAbstract
Contractive selfadjoint extensions of a Hermitian contraction $B$ in a Hilbert space $\mathfrak H$ with an exit in some larger Hilbert space $\mathfrak H\oplus\mathcal H$ are investigated. This leads to a new geometric approach for characterizing analytic properties of holomorphic operator-valued functions of Krein-Ovcharenko type, a class of functions whose study has been recently initiated by the authors. Compressed resolvents of such exit space extensions are also investigated leading to some new connections to transfer functions of passive discrete-time systems and related classes of holomorphic operator-valued functions.References
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