Differentiation of Singular Integrals with Piecewise-Continuous Density and Boundary Values of Derivatives of a Cauchy-Type Integral
Abstract
We establish sufficient conditions for the differentiability of a singular Cauchy integral with piecewise-continuous density. Formulas for the nth-order derivatives of a singular Cauchy integral and for the boundary values of the nth-order derivatives of a Cauchy-type integral are obtained.
English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 2, pp 261-270.
Citation Example: Plaksa S. A. Differentiation of Singular Integrals with Piecewise-Continuous Density and Boundary Values of Derivatives of a Cauchy-Type Integral // Ukr. Mat. Zh. - 2005. - 57, № 2. - pp. 222–229.
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