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Principal Values of Cauchy Integrals, Rectifiable Measures and Sets
1991The extensive studies started by A. P. Calderon in the sixties and continued by many authors up today have revealed that the Cauchy integrals $$ {C_{\Gamma }}f(z) = \int_{\Gamma } {\frac{{f\left( \zeta \right)d\zeta }}{{\zeta - z}}} $$ behave very well on sufficiently regular, not necessarily smooth, curves F, see [CCFJR], [D] and [MT].
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Repeated Integrals Involving Cauchy Principal Values
Journal of the London Mathematical Society, 1950openaire +2 more sources
Uniform convergence of optimal order quadrature rules for Cauchy principal value integrals
Journal of Computational and Applied Mathematics, 1994Kai Diethelm
exaly
An algorithm for the numerical evaluation of certain Cauchy principal value integrals
Numerische Mathematik, 1972Elliott David
exaly
A Note on Quadrature Formulae for Cauchy Principal Value Integrals
IMA Journal of Applied Mathematics, 1980openaire +1 more source
Uniform error bounds for Cauchy principal value integrals
2004In this paper the author provides a uniform convergence result in the numerical evaluation of weighted Cauchy principal value integrals of kind \[ I(\omega_{\alpha\beta}f;\lambda)=\int_J \text{\kern-12pt\(-\)}\;\omega_{\alpha\beta}(x){{f(x)}\over{x-\lambda}}\;dx, \] where \(J:=[-1,1]\), \(\lambda\in(-1,1)\) and \(\omega_{\alpha\beta}\) is the Jacobi ...
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