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Integration over a fractal curve and the jump problem

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Abstract

A definition of integration, i.e., a generalization of a functional of the form

$$u(z) \mapsto \smallint _\Gamma f(z)u(z) dz$$

to the case where Γ is a fractal curve on the complex plane andƒ(z) (integration density) is a function defined on this curve is given. The existence and uniqueness of the integral with given density are examined.

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Authors and Affiliations

  1. Kazan State Academy of Building and Architecture, USSR

    B. A. Kats

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  1. B. A. Kats
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Additional information

Translated fromMatematicheskie Zametki, Vol. 64, No. 4, pp. 549–557, October, 1998.

This research was supported by the Russian Foundation for Basic Research under grant No. 95-01-00674.

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Kats, B.A. Integration over a fractal curve and the jump problem. Math Notes 64, 476–482 (1998). https://doi.org/10.1007/BF02314628

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  • DOI: https://doi.org/10.1007/BF02314628

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