Singular integral equations of volterra type and the finite part of divergent integrals

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1959 English Publisher:Springer Science and Business Media LLCJournal:Archive for Rational Mechanics and Analysis, volume 3, pages 194-205 (issn: 0003-9527, eissn: 1432-0673,

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Authors: Butzer, Paul L.;

doi: 10.1007/bf00284175

Singular integral equations of volterra type and the finite part of divergent integrals

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Abstract

of the first and second kind respectively for integral and non-integral values of a ~ t z. In the more,common case 0c 1 an interpretation of the divergent integrals may be sought by CAUCH.Y'S principal values for a ~-t and HADAMARD'S finite parts for a > t. Equations of this type occur in aerodynamics, as for example the Prandtl equation in airfoil theory. According to HADAMARD [71 we have the definition t--e ] f [(1(,,) du (t.t) F P /(u) -du = lim -

Keywords

integral equations, integral transforms

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