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Abstract: We prove Strichartz estimates for the absolutely continuous evolution of aSchr\-odinger operator $H = i abla + A^2 + V$ in $\R^n$, $n > 2$. Both themagnetic and electric potentials are time-independent and satisfy pointwisepolynomial decay bounds. The vector potential $Ax$ is assumed to becontinuous but need not possess any Sobolev regularity. This work is arefinement of previous methods, which required extra conditions on ${ m div}A$ or $| abla|^{\frac12}A$ in order to place the first order part of theperturbation within a suitable class of pseudo-differential operators.



Author: Michael Goldberg

Source: https://arxiv.org/



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