# 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} }

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

Semiclassical Resolvent Bounds for Long-Range Lipschitz Potentials

- MathematicsInternational Mathematics Research Notices
- 2021

We give an elementary proof of weighted resolvent estimates for the semiclassical Schrödinger operator $-h^2 \Delta + V(x) - E$ in dimension $n \neq 2$, where $h, \, E> 0$. The potential is real…

Improved resolvent bounds for radial potentials. II

- Mathematics
- 2022

We prove semiclassical resolvent estimates for the Schrödinger operator in R, d ≥ 3, with real-valued radial potentials V ∈ L(R). We show that if V (x) = O ( 〈x〉 ) with δ > 4, then the resolvent…

Semiclassical resolvent bounds for compactly supported radial potentials

- Mathematics
- 2021

We employ separation of variables to prove weighted resolvent estimates for the semiclassical Schrödinger operator −h∆ + V (|x|) − E in dimension n ≥ 2, where h, E > 0, and V : [0,∞) → R is L and…

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