We consider a Schr\"odinger hamiltonian $H$ with scaling critical and time independent external electromagnetic potential, and assume that the angular operator $L$ associated to $H$ is positively definite. We prove the following: if $\|e^{-itH}\|_{L^1\to L^\infty}\leq Ct^{-n/2}$, then $ \||x|^{-g(n)}e^{-itH}|x|^{-g(n)}\|_{L^1\to L^\infty}\leq Ct^{-n/2-g(n)}$, being $g(n)$ a positive number, explicitly depending on the ground level of $L$ and the space dimension $n$.

Improved time-decay for a class of scaling critical electromagnetic Schrödinger flows / Fanelli, Luca; Grillo, Gabriele; Kovařík, Hynek. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - STAMPA. - 269:10(2015), pp. 3336-3346. [10.1016/j.jfa.2015.07.008]

Improved time-decay for a class of scaling critical electromagnetic Schrödinger flows

FANELLI, Luca;
2015

Abstract

We consider a Schr\"odinger hamiltonian $H$ with scaling critical and time independent external electromagnetic potential, and assume that the angular operator $L$ associated to $H$ is positively definite. We prove the following: if $\|e^{-itH}\|_{L^1\to L^\infty}\leq Ct^{-n/2}$, then $ \||x|^{-g(n)}e^{-itH}|x|^{-g(n)}\|_{L^1\to L^\infty}\leq Ct^{-n/2-g(n)}$, being $g(n)$ a positive number, explicitly depending on the ground level of $L$ and the space dimension $n$.
2015
Decay estimates; Electromagnetic potentials; Representation formulas; Schrödinger equation; Analysis
01 Pubblicazione su rivista::01a Articolo in rivista
Improved time-decay for a class of scaling critical electromagnetic Schrödinger flows / Fanelli, Luca; Grillo, Gabriele; Kovařík, Hynek. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - STAMPA. - 269:10(2015), pp. 3336-3346. [10.1016/j.jfa.2015.07.008]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/832703
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