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Mat. Zametki, 1973, Volume 14, Issue 5, Pages 677–685 (Mi mz9952)  

Boundary-value problem of arleman with a noninvolutory shift

A. V. Aizenshtat, V. A. Chernetskii

Odessa State University

Abstract: By a conformal pasting method we reduce the Carleman boundary-value problem
$$ \Phi^+[\alpha(t)]=G(t)\Phi^+(t)+g(t) $$
with a nonconvergent shift $\alpha(t)$ ($\alpha[\alpha(t)]\not\equiv t$) to the problem of finding all analytic functions which are simultaneously the solutions of two problems on an open contour: the Riemann problem and the Hasemann problem. Using this reduction, we obtain a theorem concerning the solvability of the stated problem.

Full text: PDF file (1304 kB)

English version:
Mathematical Notes, 1973, 14:5, 948–952

Bibliographic databases:

UDC: 517
Received: 19.02.1973

Citation: A. V. Aizenshtat, V. A. Chernetskii, “Boundary-value problem of arleman with a noninvolutory shift”, Mat. Zametki, 14:5 (1973), 677–685; Math. Notes, 14:5 (1973), 948–952

Citation in format AMSBIB
\Bibitem{AizChe73}
\by A.~V.~Aizenshtat, V.~A.~Chernetskii
\paper Boundary-value problem of arleman with a noninvolutory shift
\jour Mat. Zametki
\yr 1973
\vol 14
\issue 5
\pages 677--685
\mathnet{http://mi.mathnet.ru/mz9952}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=342713}
\zmath{https://zbmath.org/?q=an:0286.30033}
\transl
\jour Math. Notes
\yr 1973
\vol 14
\issue 5
\pages 948--952
\crossref{https://doi.org/10.1007/BF01462255}


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