This article is cited in 10 papers

Integration over a fractal curve and the jump problem

B. A. Kats

Kazan State Academy of Architecture and Construction

Abstract: A definition of integration, i.e., a generalization of a functional of the form
$$ u(z)\mapsto\int_\Gamma f(z)u(z)dz $$
to the case where $\Gamma$ is a fractal curve on the complex plane and $f(z)$ (integration density) is a function defined on this curve is given. The existence and uniqueness of the integral with given density are examined.

UDC: 517.9

Received: 17.07.1996
Revised: 20.11.1997

DOI: 10.4213/mzm1429

 English version: Mathematical Notes, 1998, 64:4, 476–482

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