Abstract:
Let $\mathrm D^+$ be a multiply connected domain bounded by a contour $\Gamma$, let $\mathrm D^-$ be the complement of
$\mathrm D^+\cup\Gamma$ in $\overline{\mathbb C}={\mathbb C}\cup\{\infty\}$,
and $a(t)$ be a continuous invertible matrix-valued function on $\Gamma$
which can be meromorphically extended into the open disconnected set $\mathrm D^-$
(as a piecewise meromorphic matrix-valued function). An explicit solution
of the Wiener-Hopf factorization problem for $a(t)$ is obtained and the partial factorization indices of
$a(t)$ are calculated. Here an explicit solution of a factorization problem is meant in the sense of reducing it to
the investigation of finitely many systems of linear algebraic equations
with matrices expressed in closed form, that is, in quadratures.
Bibliography: 15 titles.
Keywords:Wiener-Hopf factorization of matrix-valued functions, Riemann boundary-value problem, partial indices.
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