Exact solution of averaging procedure over the Cantor set

A.A. Stanislavsky and K. Weron

Physica A: Statistical Mechanics and its Applications, 2002, vol. 303, issue 1, 57-66

Abstract: Using functional equations with self-similar properties, we have derived the exact analytical result for convolution of a smooth function with the normalized density of the Cantor set in the limit N→∞. We have proved that the self-similar kernel of this convolution cannot be reduced explicitly to any product of a power and a log-periodic function as suggested in literature. Only its asymptotic behaviour can be expressed in terms of such a product. This clarifies the relationship between fractals and fractional calculus.

Keywords: Memory function; Cantor set; Self-similar relation; Log-periodic function; Fractional calculus (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:303:y:2002:i:1:p:57-66

DOI: 10.1016/S0378-4371(01)00487-3

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