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Fractal tube formulas and a Minkowski measurability criterion for compact subsets of Euclidean spaces


Lapidus, Michel L.; Radunović, Goran; Žubrinić Darko
Fractal tube formulas and a Minkowski measurability criterion for compact subsets of Euclidean spaces // Discrete and Continuous Dynamical Systems-Series S, 12 (2019), 1; 105-117 doi:10.3934/dcdss.2019007 (međunarodna recenzija, članak, znanstveni)


Naslov
Fractal tube formulas and a Minkowski measurability criterion for compact subsets of Euclidean spaces

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

Izvornik
Discrete and Continuous Dynamical Systems-Series S (1937-1632) 12 (2019), 1; 105-117

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Distance zeta function ; Minkowski dimension ; Minkowski measurability ; complex dimensions

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika



POVEZANOST RADA


Projekt / tema
HRZZ-IP-2014-09-2285 - Geometrijska, ergodička i topološk a analiza nisko-dimenzionalnih dinamičkih sustava (Siniša Slijepčević, )

Ustanove
Fakultet elektrotehnike i računarstva, Zagreb

Časopis indeksira:


  • Current Contents Connect (CCC)
  • Web of Science Core Collection (WoSCC)
    • Science Citation Index Expanded (SCI-EXP)
    • SCI-EXP, SSCI i/ili A&HCI
  • Scopus


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