Dispersive estimates for Schrodinger operators in dimensions one and three
arXiv:math/0306108 · doi:10.1007/s00220-004-1140-5
Abstract
We prove L^1 --> L^\infty estimates for linear Schroedinger equations in dimensions one and three. The potentials are only required to satisfy some mild decay assumptions. No regularity on the potentials is assumed.
20 pages. Corrected typos and improved explanatory remarks at the end
Cited by in corpus (76)
- Selection of the ground state for nonlinear Schroedinger equations
- Kink dynamics in the model: asymptotic stability for odd perturbations in the energy space
- Dispersive estimates for Schroedinger operators in dimension two
- Lyapunov control of a quantum particle in a decaying potential
- L^p boundedness of the wave operator for the one dimensional Schroedinger operator
- Schrödinger dispersive estimates for a scaling-critical class of potentials
- On the spectral theory and dispersive estimates for a discrete Schrödinger equation in one dimension
- Dispersive Estimates for higher dimensional Schrödinger Operators with threshold eigenvalues I: The odd dimensional case
- Dispersion Estimates for One-dimensional Discrete Schrödinger and Wave Equations
- Dispersive estimates for four dimensional Schrödinger and wave equations with obstructions at zero energy
- Stable manifolds for an orbitally unstable NLS
- Quadratic Klein-Gordon equations with a potential in one dimension
- A counterexample to dispersive estimates for Schrödinger operators in higher dimensions
- Time decay of scaling invariant Schroedinger equations on the plane
- The d nonlinear Schrödinger equation with a weighted potential
- A weighted dispersive estimate for Schrödinger operators in dimension two
- On the Fourth order Schrödinger equation in three dimensions: dispersive estimates and zero energy resonances
- Dispersive estimate for the Schroedinger equation with point interactions
- On pointwise decay of waves
- On asymptotic stability of standing waves of discrete Schrödinger equation in
- Asymptotic stability of small solitons to 1D NLS with potential
- Dispersion Estimates for One-Dimensional Discrete Dirac Equations
- Asymptotic stability of ground states in 2D nonlinear Schrödinger equation including subcritical cases
- Dispersion for the Schrödinger equation on the line with multiple Dirac delta potentials and on delta trees
- On the boundedness of wave operators for two-dimensional Schrödinger operators with threshold obstructions
- The boundedness of wave operators for Schrödinger operators with threshold singularities II. Even dimensional case
- Stable manifolds for all monic supercritical NLS in one dimension
- A weighted estimate for two dimensional Schrodinger, matrix schrodinger and wave equations with resonance of first kind at zero energy
- On the one dimensional Dirac equation with potential
- Time decay estimates for the wave equation with potential in dimension two
- Dispersion Estimates for One-Dimensional Schrödinger Equations with Singular Potentials
- Resolvent expansion and time decay of the wave functions for two-dimensional magnetic Schroedinger operators
- Abstract theory of decay estimates: perturbed Hamiltonians
- Bilinear estimates in the presence of a large potential and a critical NLS in 3d
- Dispersive Estimates for Scalar and Matrix Schrödinger operators on
- Spectral Theory and Nonlinear PDE: a Survey
- Asymptotic stability of small gap solitons in the nonlinear Dirac equations
- Low frequency dispersive estimates for the Schrodinger group in higher dimensions
- Asymptotic Stability and Completeness in the Energy Space for Nonlinear Schrödinger Equations with Small Solitary Waves
- Dispersion Estimates for One-Dimensional Schrödinger and Klein-Gordon Equations Revisited
- Dispersive Estimates in R^3 with Threshold Resonances
- Dispersive effects and high frequency behaviour for the Schrödinger equation in star-shaped networks
- Dispersive estimates for Schroedinger operators: A survey
- Decay for the wave and Schroedinger evolutions on manifolds with conical ends, Part II
- Dispersive estimates for Schroedinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three: II
- Scattering for NLS with a potential on the line
- Long-time dynamics of small solutions to 1 cubic nonlinear Schrödinger equations with a trapping potential
- Asymptotic stability of small bound state of nonlinear quantum walks
- The Nonlinear Schrodinger equation with a potential in dimension 1
- Dispersive estimates for matrix Schrödinger operators in dimension two
- Semiclassical analysis of low and zero energy scattering for one dimensional Schrödinger operators with inverse square potentials
- Spectral multipliers for Schrödinger operators
- Decay estimates for the Schroedinger evolution on asymptotically conic surfaces of revolution I
- Time decay of scaling critical electromagnetic Schrödinger flows
- continuity of wave operators in
- estimates for matrix Schrödinger equations
- Decay estimates for the wave and Dirac equations with a magnetic potential
- Dispersion Estimates for Spherical Schrödinger Equations with Critical Angular Momentum
- Explicit error estimates for the stationary phase method II: Interaction of amplitude singularities with stationary points
- Lossless error estimates for the stationary phase method with applications to propagation features for the Schrödinger equation
- Dispersive estimates and NLS on product manifolds
- On -Isomonodromic Deformations and -Nekrasov Functions
- Time-asymptotic propagation of approximate solutions of Schrödinger equations with both potential and initial condition in Fourier-frequency bands
- Decay estimates for higher order elliptic operators
- The Massless Dirac Equation in Three Dimensions: Dispersive estimates and zero energy obstructions
- Dispersive estimates for inhomogeneous fourth-order Schrödinger operator in 3D with zero energy obstructions
- A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations
- Double Scattering Channels for NLS in the Energy Space and its Generalization to Higher Dimensions
- On instability of some approximate periodic solutions for the full nonlinear Schrödinger equation
- The L^p-continuity of the wave operators for the three dimensional Schroedinger operator
- Decay estimates for fourth-order Schrödinger operators in dimension two
- A Spectral Multiplier Theorem associated with a Schrödinger Operator
- A Remark on Littlewood-Paley projections
- Global Strichartz estimates for an inhomogeneous Maxwell system
- Strichartz and Smoothing Estimates for Schroedinger Operators with Large Magnetic Potentials in R^3
- Strichartz estimates for the magnetic Schrödinger equation with potentials of critical decay