On a class of Model Hilbert Spaces
arXiv:1111.0645
Abstract
We provide a detailed description of the model Hilbert space $L^2(\bbR; dΣ; \cK)$, were $\cK$ represents a complex, separable Hilbert space, and 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.
23 pages