Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Essentially coercive forms and asympotically compact semigroups   Form methods are most efficient to prove generation theorems for semigroups
but also for proving selfadjointness. So far those theorems are based on a
coercivity notion which allows the use of the Lax-Milgram Lemma. Here we
consider weaker "essential" versions of coerciveness which already suffice to
obtain the generator of a semigroup S or a selfadjoint operator. We also show
that one of these properties, namely essentially positive coerciveness implies
a very special asymptotic behaviour of S, namely asymptotic compactness; i.e.
that dist(S(t),K(H)) tends to 0 as t tends to infinity, where K(H) denotes the
space of all compact operators on the underlying Hilbert space.

30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin