Asymptotics of spectrum under infinitesimally form-bounded perturbation

LetA1 be a selfadjoint operator with discrete spectrum and known distribution function of its spectrumN(r,A). SupposeB is a (nonselfadjoint) operator that is form-bounded with respect toA with relative bound zero. If in addition thenN(r,A+B)=N(r,A)(1+o(1)), whereA+B is the operator defined as form sum. The applications to the Schrödinger operator with polynomially growing potential and to the third boundary value problem for the second order elliptic operator are given.Research supported by the Israel Ministries of Science and Absorption