Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decay estimates for higher order elliptic operators   This paper is mainly devoted to study time decay estimates of the
higher-order Schr\"{o}dinger type operator $H=(-\Delta)^{m}+V(x)$ in
$\mathbf{R}^{n}$ for $n>2m$ and $m\in\mathbf{N}$. For certain decay potentials
$V(x)$, we first derive the asymptotic expansions of resolvent $R_{V}(z)$ near
zero threshold with the presence of zero resonance or zero eigenvalue, as well
identify the resonance space for each kind of zero resonance which displays
different effects on time decay rate. Then we establish Kato-Jensen type
estimates and local decay estimates for higher order Schr\"odinger propagator
$e^{-itH}$ in the presence of zero resonance or zero eigenvalue. As a
consequence, the endpoint Strichartz estimate and $L^{p}$-decay estimates can
also be obtained. Finally, by a virial argument, a criterion on the absence of
positive embedded eigenvalues is given for $(-\Delta)^{m}+V(x)$ with a
repulsive potential.

36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an