Naslov
A Minkowski measurability criterion for relative fractal drums via complex dimensions

Autori
Lapidus, Michel L. ; Radunović, Goran ; Žubrinić, Darko

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
6th Croatian Mathematical Congress: Book of Abstracts / - Zagreb, 2016

Skup
6th Croatian Mathematical Congress

Mjesto i datum
Zagreb, Hrvatska, 14.06.2016. - 17.06.2016

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
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

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA