Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on perturbations of $C_0$-semigroups   This article deals with a variation of constants type inequality for
semigroups acting consistently on a scale of Banach spaces. This inequality can
be characterized by a corresponding (easy to verify) inequality for their
generators. The results have applications to heat kernel estimates and provide
a unified perspective to estimates of these type. Moreover, bi-continuous
semigroups can be treated as well.

11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
16
The categories of this paper are: stat
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th