Fractal tube formulas and a Minkowski measurability criterion for compact subsets of Euclidean spaces (CROSBI ID 227239)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Lapidus, Michel L. ; Radunović, Goran ; Žubrinić, Darko
engleski
Fractal tube formulas and a Minkowski measurability criterion for compact subsets of Euclidean spaces
We establish pointwise and distributional fractal tube formulas for a large class of compact subsets of Euclidean spaces of arbitrary dimensions. These formulas are expressed as sums of residues of suitable meromorphic functions over the complex dimensions of the compact set under consideration (i.e., over the poles of its fractal zeta function). Our results generalize to higher dimensions (and in a significant way) the corresponding ones previously obtained for fractal strings by the first author and van Frankenhuijsen. They are illustrated by several examples and applied to yield a new Minkowski measurability criterion.
distance zeta function ; Minkowski dimension ; Minkowski measurability ; complex dimensions
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Podaci o izdanju
12 (1)
2019.
105-117
objavljeno
1937-1632
1937-1179
10.3934/dcdss.2019007