$N^\pm$-integrals and boundary values of Cauchy-type integrals of finite measures
Sbornik. Mathematics, Tome 205 (2014) no. 7, pp. 913-935
Voir la notice de l'article provenant de la source Math-Net.Ru
Let $\Gamma $ be a simple closed Lyapunov contour with finite complex measure $\nu$, and let $G^+ $ be the bounded and $G^- $ the unbounded domains with boundary $\Gamma$. Using new notions (so-called $N$-integration and $N^+$- and $N^-$-integrals), we prove that the Cauchy-type integrals $F^+(z)$, $z\in G^+$, and $F^-(z)$, $z\in G^-$, of $\nu $ are Cauchy $N^+$- and $N^-$-integrals, respectively. In the proof of the corresponding results, the additivity property and the validity of the change-of-variable formula for the $N^+$- and $N^-$-integrals play an essential role.
Bibliography: 21 titles.
Keywords:
finite complex Borel measure, Cauchy-type integral, nontangential boundary values, Cauchy integral, $Q$-integral, $Q'$-integral, $N$-integration.
@article{SM_2014_205_7_a0,
author = {R. A. Aliyev},
title = {$N^\pm$-integrals and boundary values of {Cauchy-type} integrals of finite measures},
journal = {Sbornik. Mathematics},
pages = {913--935},
publisher = {mathdoc},
volume = {205},
number = {7},
year = {2014},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2014_205_7_a0/}
}
R. A. Aliyev. $N^\pm$-integrals and boundary values of Cauchy-type integrals of finite measures. Sbornik. Mathematics, Tome 205 (2014) no. 7, pp. 913-935. http://geodesic.mathdoc.fr/item/SM_2014_205_7_a0/