Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Operators $L^1 (\mathbb R_+ )\to X$ and the norm continuity problem for
  semigroups   We present a new method for constructing $C_0$-semigroups for which
properties of the resolvent of the generator and continuity properties of the
semigroup in the operator-norm topology are controlled simultaneously. It
allows us to show that a) there exists a $C_0$-semigroup which is continuous in
the operator-norm topology for no $t \in [0,1]$ such that the resolvent of its
generator has a logarithmic decay at infinity along vertical lines; b) there
exists a $C_0$-semigroup which is continuous in the operator-norm topology for
no $t \in \mathbb R_+$ such that the resolvent of its generator has a decay
along vertical lines arbitrarily close to a logarithmic one. These examples
rule out any possibility of characterizing norm-continuity of semigroups on
arbitrary Banach spaces in terms of resolvent-norm decay on vertical lines.

23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin