New Estimates for a Time-Dependent Schroedinger Equation

Abstract

This paper establishes new estimates for linear Schroedinger equations in R^3 with time-dependent potentials. Some of the results are new even in the time-independent case and all are shown to hold for potentials in scaling-critical, translation-invariant spaces. The proof of the time-independent results uses a novel method based on an abstract version of Wiener's Theorem.

49 pages; this is an expanded and improved version of the older paper

References in corpus (6)

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Cited by in corpus (16)

• Schrödinger dispersive estimates for a scaling-critical class of potentials
• Strichartz Estimates and Maximal Operators for the Wave Equation in R^3
• On pointwise decay of waves
• Codimension one threshold manifold for the critical gKdV equation
• Freezing of energy of a soliton in an external potential
• Strichartz estimates for Schrödinger equations with slowly decaying potentials
• Uniform Sobolev estimates for Schrödinger operators with scaling-critical potentials and applications
• Dispersive Estimates in R^3 with Threshold Resonances
• The Zakharov system in 4D radial energy space below the ground state
• Wave equations with moving potentials
• Dispersive estimates for higher order Schrödinger operators with scaling-critical potentials
• Asymptotic stability of solitons to 1D Nonlinear Schrodinger Equations in subcritical case
• L^p Boundedness of the Scattering Wave Operators of Schroedinger Dynamics with Time-dependent Potentials and applications
• Inhomogeneous Strichartz estimates in some critical cases
• Invariant manifolds around soliton manifolds for the nonlinear Klein-Gordon equation
• Modified scattering for nonlinear Schrödinger equations with long-range potentials