SMOOTH RANK-ONE PERTURBATIONS OF SELF-ADJOINT OPERATORS

Let A be a selfadjoint operator in a Hilbert space aleph with inner pr oduct [.,.]. The rank one perturbations of A have the form A+tau [.,om ega]omega, tau epsilon R, for some element omega epsilon aleph. In thi s paper we consider smooth perturbations, i.e. we consider omega epsil on dom \A\(k/2) for some k epsilon N boolean OR {0}. Function-theoreti c properties of their so-called Q-functions and operator-theoretic con sequences will be studied.