Geodesic
On certain one- and two-dimensional hypersingular integral equations
Sbornik. Mathematics, Tome 192 (2001) no. 8, pp. 1089-1131 Cet article a éte moissonné depuis la source Math-Net.Ru

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For two-dimensional singular and hypersingular integrals more general definitions than the traditional ones are introduced. For a hypersingular operator on a sphere a new spectral relation is obtained. Quadrature formulae of the kind of discrete vortex pairs for one-dimensional and of the kind of closed vortex frames for two-dimensional hypersingular integrals are considered; questions on their convergence are discussed, as well as the convergence of numerical solutions to the corresponding hypersingular integral equations on a finite line interval and a circle. An experiment on the numerical solution of a hypersingular integral equation on a sphere is carried out, which demonstrates analogies between numerical solutions of hypersingular integral equations on a finite interval and a sphere. 
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A. Yu. Anfinogenov; I. K. Lifanov; P. I. Lifanov. On certain one- and two-dimensional hypersingular integral equations. Sbornik. Mathematics, Tome 192 (2001) no. 8, pp. 1089-1131. http://geodesic.mathdoc.fr/item/SM_2001_192_8_a0/

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