Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smooth measures and capacities associated with nonlocal parabolic
  operators   We consider a family $\{L_t,\, t\in [0,T]\}$ of closed operators generated by
a family of regular (non-symmetric) Dirichlet forms $\{(B^{(t)},V),t\in[0,T]\}$
on $L^2(E;m)$. We show that a bounded (signed) measure $\mu$ on $(0,T)\times E$
is smooth, i.e. charges no set of zero parabolic capacity associated with
$\frac{\partial}{\partial t}+L_t$, if and only if $\mu$ is of the form
$\mu=f\cdot m_1+g_1+\partial_tg_2$ with $f\in L^1((0,T)\times E;dt\otimes m)$,
$g_1\in L^2(0,T;V')$, $g_2\in L^2(0,T;V)$. We apply this decomposition to the
study of the structure of additive functionals in the Revuz correspondence with
smooth measures. As a by-product, we also give some existence and uniqueness
results for solutions of semilinear equations involving the operator
$\frac{\partial}{\partial t}+L_t$ and a functional from the dual $\mathcal{W}'$
of the space $\mathcal{W}=\{u\in L^2(0,T;V):\partial_t u\in L^2(0,T;V')\}$ on
the right-hand side of the equation.

35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int