Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gaussian Estimates for Heat Kernels of Higher Order Schr\"odinger
  Operators with Potentials in Generalized Schechter Classes   Let $m\in\mathbb N$, $P(D):=\sum_{|\alpha|=2m}(-1)^m a_\alpha D^\alpha$ be a
$2m$-order homogeneous elliptic operator with real constant coefficients on
$\mathbb{R}^n$, and $V$ a measurable function on $\mathbb{R}^n$. In this
article, the authors introduce a new generalized Schechter class concerning $V$
and show that the higher order Schr\"odinger operator $\mathcal{L}:=P(D)+V$
possesses a heat kernel that satisfies the Gaussian upper bound and the
H\"older regularity when $V$ belongs to this new class. The Davies--Gaffney
estimates for the associated semigroup and their local versions are also given.
These results pave the way for many further studies on the analysis of
$\mathcal{L}$.

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The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph