Resolvent estimates on symmetric spaces of noncompact type (Q743695)

The author establishes a resolvent estimate for the Laplace-Beltrami operator or more general elliptic Fouirer multipliers on symmetric spaces of noncompact type. Then Kato theory implies time-global smoothing estimates for the corresponding dispersive equations, especially the Schrödinger evolution equation. For low-frequency estimates, a pseudo-dimension appears as an upper bound of the order of elliptic Fourier multipliers. A key of the proof is to show weighted \(L^2\)-continuity of the modified Radon transform and fractional integral operators.