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Chebyshev-Hilbert transform method for the solution of singular integrals and singular integral equations. (English) Zbl 0871.45004

The authors present several schemes in the approach to the problem of evaluating the singular integrals of Cauchy type. The approach is based on some properties of Chebyshev polynomials and the solution of the problem is obtained in the polynomial form with a strong convergence. The results are applied to the singular integral equations and demonstrated with the infinite medium and half-space problems in radiation transport.

MSC:

45E05 Integral equations with kernels of Cauchy type
85A25 Radiative transfer in astronomy and astrophysics
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