Spherical Schrödinger hamiltonians: spectral analysis and time decay

In this survey, we review recent results concerning the canonical dispersive flow e^(itH) led by a Schrödinger Hamiltonian H. We study, in particular, how the time decay of space Lp-norms depends on the frequency localization of the initial datum with respect to the some suitable spherical expansion. A quite complete description of the phenomenon is given in terms of the eigenvalues and eigenfunctions of the restriction of H to the unit sphere, and a comparison with some uncertainty inequality is presented. © Springer International Publishing AG 2017.