NEGATIVE EIGENVALUES OF NON-LOCAL SCHRoDINGER OPERATORS WITH SIGN-CHANGING POTENTIALS

Simon's results on the negative spectrum of recurrent Schrodinger operators (d " 1,2) are extended to a wider class of potentials and to non-lo cal operators. An example of L1 & PRIME;potental is constructed for which the essential spectrum of two dimensional Schrodinger operator covers the whole axis. Some counterexamples are provided for transient operators (d e 3) showing that the assumptions on the potential for the validity of the Cwikel-Lieb-Rozenblum estimate can't be improved significantly.