Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Resolvent estimates for one-dimensional Schr\"odinger operators with
  complex potentials   We study one-dimensional Schr\"odinger operators $\operatorname{H} =
-\partial_x^2 + V$ with unbounded complex potentials $V$ and derive asymptotic
estimates for the norm of the resolvent, $\Psi(\lambda) := \| (\operatorname{H}
- \lambda)^{-1} \|$, as $|\lambda| \to +\infty$, separately considering
$\lambda \in \operatorname{Ran} V$ and $\lambda \in \mathbb{R}_+$. In each
case, our analysis yields an exact leading order term and an explicit remainder
for $\Psi(\lambda)$ and we show these estimates to be optimal. We also discuss
several extensions of the main results, their interrelation with some aspects
of semigroup theory and illustrate them with examples.

17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int