SCHRODINGER-OPERATORS WITH FAIRLY ARBITRARY SPECTRAL FEATURES

It is shown, using methods of inverse-spectral theory, that there exis t Schrodinger operators on the line with fairly general spectral featu res. Thus, for instance, it follows from the main theorem, that if Sig ma is any perfect subset of (-infinity,0], then there exist potentials q(j),j = 1,2 such that the associated Schrodinger operators H-j are s elf-adjoint and satisfy: sigma(H-j) = Sigma boolean OR, [0, infinity), sigma(ac)(H-j) [0, infinity), sigma(pp)(H-1) = sigma(sc)(H-2) = Sigma . The main result also implies the existence of states with interestin g transport properties.