Rank one perturbations and singular integral operators

Constanze Liaw, Sergei Treil

We consider rank one perturbations $A_{\alpha }=A+\alpha (\cdot ,\phi )\phi$ of a self-adjoint operator $A$ with cyclic vector $\phi \in {\mathcal{H}}_{-1}(A)$ on a Hilbert space $\mathcal{H}$. The spectral repr…