engleski

A Minkowski measurability criterion for relative fractal drums via complex dimensions

We establish a Minkowski measurability criterion for a large class of relative fractal drums or, in short RFDs, in Euclidean spaces of arbitrary dimension in terms of their complex dimensions. The complex dimensions are defined as poles or, more generally, singularities of their associated Lapidus fractal zeta functions. Relative fractal drums represent a far reaching generalization of bounded subsets of Euclidean spaces as well as of fractal strings. In fact, the Minkowski measurability criterion established here is a generalization of the corresponding one obtained for fractal strings by M. L. Lapidus and M. van Frankenhuijsen. We illustrate the obtained criterion on a number of interesting examples.

Mellin transform; complex dimensions of a relative fractal drum; relative fractal drum; fractal set; box dimension; fractal zeta function; distance zeta function; tube zeta function; fractal string; Minkowski content; Minkowski measurable set; fractal tube formula; residue; meromorphic extension

nije evidentirano