Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pluripotential Theory and Convex Bodies: A Siciak-Zaharjuta theorem   We work in the setting of weighted pluripotential theory arising from
polynomials associated to a convex body $P$ in $({\bf R}^+)^d$. We define the
{\it logarithmic indicator function} on ${\bf C}^d$: $$H_P(z):=\sup_{ J\in P}
\log |z^{ J}|:=\sup_{ J\in P} \log[|z_1|^{ j_1}\cdots |z_d|^{ j_d}]$$ and an
associated class of plurisubharmonic (psh) functions: $$L_P:=\{u\in PSH({\bf
C}^d): u(z)- H_P(z) =0(1), \ |z| \to \infty \}.$$ We first show that $L_P$ is
not closed under standard smoothing operations. However, utilizing a continuous
regularization due to Ferrier which preserves $L_P$, we prove a general
Siciak-Zaharjuta type-result in our $P-$setting: the weighted $P-$extremal
function $$V_{P,K,Q}(z):=\sup \{u(z):u\in L_P, \ u\leq Q \ \hbox{on} \ K\}$$
associated to a compact set $K$ and an admissible weight $Q$ on $K$ can be
obtained using the subclass of $L_P$ arising from functions of the form
$\frac{1}{deg_P(p)}\log |p|$ (appropriately normalized).

23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ