Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Clark measures and de Branges-Rovnyak spaces in several variables   Let $B_n$ denote the unit ball of $\mathbb{C}^n$, $n\ge 1$, and let
$\mathcal{D}$ denote a finite product of $B_{n_j}$, $j\ge 1$. Given a
non-constant holomorphic function $b: \mathcal{D} \to B_1$, we study the
corresponding family $\sigma_\alpha[b]$, $\alpha\in\partial B_1$, of Clark
measures on the distinguished boundary $\partial\mathcal{D}$. We construct a
natural unitary operator from the de Branges-Rovnyak space $\mathcal{H}(b)$
onto the Hardy space $H^2(\sigma_\alpha)$. As an application, for $\mathcal{D}=
B_n$ and an inner function $I: B_n \to B_1$, we show that the property
$\sigma_1[I]\ll\sigma_1[b]$ is directly related to the membership of an
appropriate explicit function in $\mathcal{H}(b)$.

21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess