Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp $L^p$ estimates for Schr\"odinger groups   Consider a non-negative self-adjoint operator $H$ in $L^2(\mathbb{R}^d)$. We
suppose that its heat operator $e^{-tH}$ satisfies an off-diagonal algebraic
decay estimate, for some exponents $p_0\in[0,2)$. Then we prove sharp $L^p\to
L^p$ frequency truncated estimates for the Schr\"odinger group $e^{itH}$ for
$p\in[p_0,p'_0]$. In particular, our results apply to every operator of the
form $H=(i\nabla+A)^2+V$, with a magnetic potential $A\in
L^2_{loc}(\mathbb{R}^d,\mathbb{R}^d)$ and an electric potential $V$ whose
positive and negative parts are in the local Kato class and in the Kato class,
respectively.

3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga