Dispersive Estimates for Schrödinger Operators in Dimensions One and Three

By M. Goldberg, Wilhelm Schlag. 2003

252 citations recorded by the source corpus.

We consider L1→L∞ estimates for the time evolution of Hamiltonians H=−Δ+V in dimensions d=1 and d=3 with bound We require decay of the potentials but no regularity. In d=1 the decay assumption is ∫(1+|x|)|V(x)|dx<∞, whereas in d=3 it is |V(x)|≤C(1+|x|)−3−.

Subfields: Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a1162feff97420a8b7149b1515688d1498429ed0

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In Mathematical Physics

Citations in the corpus

Dispersive Estimates for Schrödinger Equations with Threshold Resonance and Eigenvalue (2005, background): “has recently been proved by Goldberg-Schlag ([ 8 ], see [12, 2, 30, 30, 31, 28, 25, 27] for earlier and related works).”
Dispersive Estimates for Four Dimensional Schrödinger and Wave Equations with Obstructions at Zero Energy (2013, background): “[37] Schlag, W. (2005).”
Strichartz and Smoothing Estimates for Dispersive Equations with Magnetic Potentials (2007, background): “We mention among the many works [7], [19], [18], [29], [31] and the survey [30] for the Schrödinger equation, and [9], [15], [13] for the wave equation.”
Dispersive Estimates for Higher Dimensional Schrödinger Operators with Threshold Eigenvalues I: The Odd Dimensional Case (2014, background): “[26] Schlag, W. Dispersive estimates for Schrödinger operators in dimension two.”
Endpoint Strichartz estimates for the magnetic Schrodinger equation (2009, background): “In the purely electric case A ≡ 0 the literature is extensive and almost complete; we may cite among many others the papers [3], [16], [25].”
Kink dynamics in the $\phi^4$ model: asymptotic stability for odd perturbations in the energy space (2015, methodology): “The method used in this paper combines dispersive estimates by Weder [42, 43] (see also [12]), together with Klainerman vectors fields and normal forms.”