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Publications Goldberg, M., and Visan, M. (2005) A counterexample to dispersive estimates for Schrödinger operators in higher dimensions. Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4 . Abstract of the Dissertation We consider the initial value problem for the defocusing energy-critical nonlinear where the initial data u 0 is chosen to belong to the energy-spaceḢ 1 (R n ), and u(t, x) is a complex-valued function in spacetime R tdoi:10.1353/ajm.0.0107 fatcat:qm3z2jbi2vh63do6qmj4edgnf4