Regular, Singular and Hypersingular Integrals over Fractal Contours
Ilya Boykov,
Vladimir Roudnev,
Alla Boykova
Abstract:The paper is devoted to the approximate calculation of Riemann definite integrals, singular and hypersingular integrals over closed and open non-rectifiable curves and fractals. The conditions of existence for the Riemann definite integrals over non-rectifiable curves and fractals are provided. We give a definition of a singular integral over non-rectifiable curves and fractals which generalizes the known one. We define hypersingular integrals over non-rectifiable curves and fractals. We construct quadratures … Show more
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