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On a method of solving integral equation of Carleman type on the pair of segments. (English) Zbl 07216511
Kravchenko, Vladislav V. (ed.) et al., Transmutation operators and applications. Cham: Birkhäuser (ISBN 978-3-030-35913-3/hbk; 978-3-030-35914-0/ebook). Trends in Mathematics, 431-445 (2020).
Summary: The method is considered of solving integral equations of Carleman type on the pair of adjacent and disjoint segments. The problem is reduced to boundary problem of Riemann with piecewise constant matrix and four and five singular points. The solution is expressed via the solution of a differential equation of Fuchs class in which it was possible to define all the parameters.
For the entire collection see [Zbl 1443.34001].
MSC:
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
34M99 Ordinary differential equations in the complex domain
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