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… 
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