# Improved resolvent bounds for radial potentials

@article{Vodev2020ImprovedRB,
title={Improved resolvent bounds for radial potentials},
author={Georgi Vodev},
journal={Letters in Mathematical Physics},
year={2020},
volume={111},
pages={1-21}
}
• G. Vodev
• Published 15 April 2020
• Mathematics
• Letters in Mathematical Physics
We prove semiclassical resolvent estimates for the Schrödinger operator in $${\mathbb {R}}^d$$ R d , $$d\ge 3$$ d ≥ 3 , with real-valued radial potentials $$V\in L^\infty ({\mathbb {R}}^d)$$ V ∈ L ∞ ( R d ) . In particular, we show that if $$V(x)={{\mathcal {O}}}\left( \langle x\rangle ^{-\delta }\right)$$ V ( x ) = O ⟨ x ⟩ - δ with $$\delta >2$$ δ > 2 , then the resolvent bound is of the form $$\exp \left( Ch^{-4/3}\right)$$ exp C h - 4 / 3 with some constant $$C>0$$ C > 0 . We also get…
3 Citations
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