Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effective Bounds for the Decay of Schr\"odinger Eigenfunctions and Agmon
  bubbles   We study solutions of $-\Delta u + V u = \lambda u$ on $\mathbb{R}^n$. Such
solutions localize in the `allowed' region $\left\{x \in \mathbb{R}^n: V(x)
\leq \lambda\right\}$ and decay exponentially in the `forbidden' region
$\left\{x \in \mathbb{R}^n: V(x) > \lambda\right\}$. One way of making this
precise is Agmon's inequality implying decay estimates in terms of the Agmon
metric. We prove a complementary decay estimate in terms of harmonic measure
which can improve on Agmon's estimate, connect the Agmon metric to decay of
harmonic measure and prove a sharp pointwise Agmon estimate.

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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
10
The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph