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Improved time-decay for a class of scaling critical electromagnetic Schrödinger flows (1502.04987v1)

Published 17 Feb 2015 in math.AP and math.SP

Abstract: We consider a Schr\"odinger hamiltonian $H(A,a)$ with scaling critical and time independent external electromagnetic potential, and assume that the angular operator $L$ associated to $H$ is positive definite. We prove the following: if $|e{-itH(A,a)}|_{L1\to L\infty}\lesssim t{-n/2}$, then $ ||x|{-g(n)}e{-itH(A,a)}|x|{-g(n)}|_{L1\to L\infty}\lesssim t{-n/2-g(n)}$, $g(n)$ being a positive number, explicitly depending on the ground level of $L$ and the space dimension $n$. We prove similar results also for the heat semi-group generated by $H(A,a)$.

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