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Dispersive estimates and NLS on product manifolds
decay estimates dispersive equations hyperbolic space
2011/1/17
We prove a general dispersive estimate for a Schr¨odinger type equation on a product manifold, under the assumption that the equation restricted to each factor satisfies suitable dispersive estimates....
Optimal dispersive estimates for the wave equation with $C^{(n-3)/2}$ potentials in dimensions $4\le n\le 7$
the wave equation math
2010/11/22
We prove optimal dispersive estimates for the wave group $e^{it\sqrt{-\Delta+V}}$ for a class of real-valued potentials $V\in C^{(n-3)/2}({\bf R}^n)$, $4\le n\le 7$, such that $\partial_x^\alpha V(x)=...
Schrödinger dispersive estimates for a scaling-critical class of potentials
Schrö dinger dispersive estimates scaling-critical class potentials
2010/12/14
We prove a dispersive estimate for the evolution of Schr¨odinger operators H = − + V (x) in R3. The potential should belong to the closure of Cc b (R3) with respsect to the global Kato norm. So...