Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Composition Operators on the Dirichlet Space and Related Problems   In this paper we investigate the following problem: when a bounded analytic
function $\phi$ on the unit disk $\mathbb{D}$, fixing 0, is such that $\{\phi^n
: n = 0, 1, 2, . . . \}$ is orthogonal in $\mathbb{D}$?, and consider the
problem of characterizing the univalent, full self-maps of $\mathbb{D}$ in
terms of the norm of the composition operator induced. The first problem is
analogous to a celebrated question asked by W. Rudin on the Hardy space setting
that was answered recently ([3] and [15]). The second problem is analogous to a
problem investigated by J. Shapiro in [14] about characterization of inner
functions in the setting of $H^2$.

24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat