On a class of Model Hilbert Spaces

We provide a detailed description of the model Hilbert space $L^2(\bbR; dΣ; \cK)$, were $\cK$ represents a complex, separable Hilbert space, and $Σ$ denotes a bounded operator-valued measure. In particular, we show that several alternative approaches to such a construction in the literature are equivalent. These spaces are of fundamental importance in the context of perturbation theory of self-adjoint extensions of symmetric operators, and the spectral theory of ordinary differential operators with operator-valued coefficients.

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