Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the spectral value of Semigroups of Holomorphic Functions   Let $(\phi_t)_{t \geq 0}$ be a semigroup of holomorphic self-maps of the unit
disk $\mathbb{D}$ with Denjoy-Wolff point $\tau=1$. The angular derivative is
$\phi_t^{\prime}(1)= e^{-\lambda t}$, where $\lambda \geq 0$ is the spectral
value of $(\phi_t)$. If $\lambda>0$ the semigroup is hyperbolic, otherwise it
is parabolic. Suppose $K$ is a compact non-polar subset of $\mathbb{D}$ with
positive logarithmic capacity. We specify the type of the semigroup by
examining the asymptotic behavior of $\phi_t(K)$. We provide a representation
of the spectral value of the semigroup with the use of several potential
theoretic quantities e.g. harmonic measure, Green function, extremal length,
condenser capacity.

7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an