This article is cited in
3 papers
Singular integral equations and the Riemann boundary value problem with infinite index in the space $L_p(\Gamma,\omega)$
S. M. Grudskii
Abstract:
The Riemann boundary value problem
$$
\varphi^+(t)-a(t)\varphi^-(t)= f(t),\qquad t\in\Gamma,
$$
is considered on a simple closed piecewise smooth contour
$\Gamma$ in the space
$L_p(\Gamma,\omega)$, along with the corresponding singular integral operator
$$
A_{a,\Gamma}=P_\Gamma^+-a(t)P_\Gamma^-
$$
with a bounded coefficient
$a(t)$ bounded away from zero and having finitely many discontinuities of the second kind that are vorticity points of power type. A theory of one-sided invertibility of
$A_{a,\Gamma}$ is constructed, the spaces
$\operatorname{Ker}A_{a,\Gamma}$ and
$\operatorname{Im}A_{a,\Gamma}$ are described, and a construction is given for the inverse operators.
Bibliography: 31 titles.
UDC:
517.948
MSC: Primary
30E25,
45E05; Secondary
30D55,
35Q15,
45E10 Received: 20.08.1982
Fulltext:
PDF file (2616 kB)
