Schrodinger Equations on Damek-Ricci Spaces

In this paper we consider the Laplace-Beltrami operator on Damek-Ricci spaces and derive pointwise estimates for the kernel of e, when * with Re epsilon 0. When i*, we obtain in particular pointwise estimates of the Schrodinger kernel associated with . We then prove Strichartz estimates for the Schrodinger equation, for a family of admissible pairs which is larger than in the Euclidean case. This extends the results obtained by Anker and Pierfelice [4] on real hyperbolic spaces. As a further application, we study the dispersive properties of the Schrodinger equation associated with a distinguished Laplacian on Damek-Ricci spaces, showing that in this case the standard L1L estimate fails while suitable weighted Strichartz estimates hold.