The mixed spectral problem for radial Schr\"{o}dinger operators and Paley-Wiener spaces

The inverse spectral problem for the radial Schr"{o}dinger operators on the finite interval is investigated. The potential is recovered from the given eigenvalues plus its information on a smaller interval. The method is to discuss the connections between the Paley-Wiener spaces and the potentials, from which we completely determine the potential on the whole interval from the potential on a smaller interval and a set of eigenvalues in terms of the complete exponential systems.