Geodesic
Direct methods for solving singular integral equations with nonnegative indices
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2008), pp. 27-39

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In this paper we consider a complete singular integral equation with the Cauchy kernel on the real axis and a bisingular integral equation on a plane with a degenerate characteristic part. We theoretically substantiate the polynomial methods of moments and collocation in the case of nonnegative indices. We also prove the convergence of the method of mechanical quadratures for the corresponding one-dimensional equation.
Keywords: singular integral on the real axis, linear one-dimensional and two-dimensional equations, direct method, convergence of a method. 
@article{IVM_2008_9_a3,
     author = {V. I. Kas'yanov},
     title = {Direct methods for solving singular integral equations with nonnegative indices},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {27--39},
     publisher = {mathdoc},
     number = {9},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_9_a3/}
}
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V. I. Kas'yanov. Direct methods for solving singular integral equations with nonnegative indices. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2008), pp. 27-39. http://geodesic.mathdoc.fr/item/IVM_2008_9_a3/