Consider the Laplacian $-\Delta$ on the hyperbolic space $\mathbb{H}^n$. For $\lambda \in \mathbb{C} \setminus [0, \infty)$, do we have resolvent estimates of the form $$\Vert (-\Delta - \lambda I)^{-1}\Vert \leq \frac{C}{|\text{Im}(\lambda)|}$$ which parallel the corresponding estimates from the Euclidean space $\mathbb{R}^n$? A reference would be highly appreciated. Thanks.
2026-03-25 17:37:36.1774460256
Resolvent estimate of hyperbolic Laplacian
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