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Tube formulas for relative fractal drums in Euclidean spaces via Lapidus zeta functions


Lapidus, Michel L.; Radunović, Goran; Žubrinić, Darko
Tube formulas for relative fractal drums in Euclidean spaces via Lapidus zeta functions // Fractals and Related Fields III
île de Porquerolles, Francuska, 2015. (poster, međunarodna recenzija, sažetak, znanstveni)


Naslov
Tube formulas for relative fractal drums in Euclidean spaces via Lapidus zeta functions

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

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

Skup
Fractals and Related Fields III

Mjesto i datum
Île de Porquerolles, Francuska, 19-25.09.2015

Vrsta sudjelovanja
Poster

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Fractal tube formula; Lapidus zeta function; Minkowski measurability

Sažetak
Relative fractal drums generalize the notion of fractal sets in Euclidean spaces of arbitrary dimension. We establish point wise and istributional fractal tube formulas for a large class of relative fractal drums. These fractal tube formulas are expressed as sums of residues of suitable meromorphic functions over the complex dimensions of the relative fractal drum under consideration (i.e., over the poles of its Lapidus zeta function which generalizes the well-known zeta function for fractal strings. These results generalize to higher dimensions the corresponding ones previously obtained for fractal strings by M. L. Lapidus and M. van Frankenhuijsen. We illustrate our results by several examples and apply them to obtain a new Minkowski measurability criterion.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Napomena
Poster je na konferenciji izložio Goran Radunović.



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