Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Data characterization in dynamical inverse problem for the 1d wave
  equation with matrix potential   The dynamical system under consideration is \begin{align*} &
u_{tt}-u_{xx}+Vu=0,\qquad x>0,\,\,\,t>0;\\ &
u|_{t=0}=u_t|_{t=0}=0,\,\,x\geqslant 0;\quad u|_{x=0}=f,\,\,t\geqslant 0,
\end{align*} where $V=V(x)$ is a matrix-valued function ({\it potential});
$f=f(t)$ is an $\mathbb R^N$-valued function of time ({\it boundary control});
$u=u^f(x,t)$ is a {\it trajectory} (an $\mathbb R^N$-valued function of $x$ and
$t$). The input/output map of the system is a {\it response operator}
$R:f\mapsto u^f_x(0,\cdot),\,\,\,t\geqslant0$.
  The {\it inverse problem} is to determine $V$ from given $R$. To characterize
its data is to provide the necessary and sufficient conditions on $R$ that
ensure its solvability.
  The procedure that solves this problem has long been known and the
characterization has been announced (Avdonin and Belishev, 1996). However, the
proof was not provided and, moreover, it turned out that the formulation must
be corrected. Our paper fills this gap.

6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn