On a class of Model Hilbert Spaces
  We provide a detailed description of the model Hilbert space $L^2(\bbR; d\Sigma; \cK)$, were $\cK$ represents a complex, separable Hilbert space, and $\Sigma$ 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. 
Fritz Gesztesy, Rudi Weikard, and Maxim Zinchenko
math.SP math-ph math.FA math.MP