Cauchy Integrals near ends of the Line of Integration

N. I. Muskhelishvili
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N. I. Muskhelishvili: Institute of Mathematics Tiflis

Chapter Chapter 4 in Singular Integral Equations, 1958, pp 73-85 from Springer

Abstract: 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.

Date: 1958
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DOI: 10.1007/978-94-009-9994-7_4

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