Title: Mixed Data in Inverse Spectral Problems for the Schrodinger Operators

Abstract: We consider the Schrodinger operator, Lu = -u''+qu on (0,\pi) with a potential q in L^1(0,\pi). Borg's theorem says that q can be uniquely recovered from two spectra. By Marchenko, q can be uniquely recovered from the spectral measure. After recalling some results from inverse spectral theory of one dimensional Schroedinger operators, we will discuss the following problem: Can q be recovered from support of the spectral measure, which is a spectrum, and partial data on another spectrum and the set of point masses of the spectral measure?