On the notion of the finite part of divergent integrals in integral equations
The paper suggests a unified approach to divergent integrals, by introducing the finite part of a divergent integral on the basis of the Taylor expansion and integration by parts. This covers all approaches considered earlier, viz. Cauchy principal value, singular integrals with finite part in the sense of Hadamard, and one-dimensional hypersingular integrals. The paper is highly theoretical, but the results obtained apply to the solution of equations containing singular integrals of the above type.
scientific article; zbMATH DE number 1916177