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Cauchy Integrals near ends of the Line of Integration

In: Singular Integral Equations

Author

Listed:
  • N. I. Muskhelishvili

    (Institute of Mathematics Tiflis)

Abstract

In this chapter some formulae and theorems on the behaviour of Cauchy integrals near the ends of the line of integration will be given. They are fundamental in the later work, whenever boundary problems or singular integral equations are considered for which the boundary or line of integration contains arcs. The results obtained below also find application in the more general case in which the density has discontinuities at several points on the line of integration. In this case the path of integration may be split up into separate arcs with the points of discontinuity as ends.

Suggested Citation

  • N. I. Muskhelishvili, 1958. "Cauchy Integrals near ends of the Line of Integration," Springer Books, in: Singular Integral Equations, chapter 0, pages 73-85, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-9994-7_4
    DOI: 10.1007/978-94-009-9994-7_4
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