We shall look at the spectral measure on asymptotically hyperbolic space with applications to spectral multiplier and Strichartz estimates.First of all,we shall talk about the resolvent on asymptotically hyperbolic space near the full continuous spectrum.Secondly,we shall show the spectral measure estimates as Stones formula gives the spectral measure on the full continuous spectrum.Next,we will link the results to Stein-Tomas restriction theorem and the boundedness of spectral multiplier,and give specific results on asymptotically hyperbolic space.In the end,we will apply the spectral measure estimates to the energy estimates and dispersive estimates for Schr(o)dinger propagator,and discuss the geometry influence on the behaviour of solutions.I will try to disentangle the essential relationship between resolvent,spectral measure,restriction theorem,spectral multiplier and dispersive estimates and to explain the specific results on asymptotically hyperbolic space,rather than to discuss the lengthy microlocal structure behind the scene.