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- Title
FRACTAL TUBE FORMULAS AND A MINKOWSKI MEASURABILITY CRITERION FOR COMPACT SUBSETS OF EUCLIDEAN SPACES.
- Authors
Lapidus, Michel L.; Radunović, Goran; Žubrinić, Darko
- Abstract
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.
- Subjects
FRACTAL analysis; MINKOWSKI geometry; MATHEMATICAL formulas; BOREL subsets; EUCLIDEAN distance; MEROMORPHIC functions
- Publication
Discrete & Continuous Dynamical Systems - Series S, 2019, Vol 12, Issue 1, p105
- ISSN
1937-1632
- Publication type
Article
- DOI
10.3934/dcdss.2019007