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Fractal tube formulas for relative fractal drums in arbitrary Euclidean spaces via Lapidus zeta functions


Lapidus, Michel L.; Radunović, Goran; Žubrinić, Darko
Fractal tube formulas for relative fractal drums in arbitrary Euclidean spaces via Lapidus zeta functions // Abstracts of Papers Presented to the American Mathematical Society / Savage, Carla D. ; Benkart, Georgia ; Boe, Brian D. ; Lapidus, Michel L. ; Weintraub, Steven H. (ur.).
Providence, RI, USA: American Mathematical Society, 2016. str. 128-129 (pozvano predavanje, međunarodna recenzija, sažetak, znanstveni)


Naslov
Fractal tube formulas for relative fractal drums in arbitrary Euclidean spaces via Lapidus zeta functions

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

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

Izvornik
Abstracts of Papers Presented to the American Mathematical Society / Savage, Carla D. ; Benkart, Georgia ; Boe, Brian D. ; Lapidus, Michel L. ; Weintraub, Steven H. - Providence, RI, USA : American Mathematical Society, 2016, 128-129

Skup
2016 Joint Mathematics Meetings: AMS Special Session on Fractal Geometry and Dynamical Systems

Mjesto i datum
Seattle, SAD, 6-9.01.2016

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Fractal tube formula; relative fractal drum; fractal zeta function; Minkowski measurability

Sažetak
Relative fractal drums generalize the notion of fractal sets in Euclidean spaces of arbitrary dimension. We establish pointwise and distributional 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 distance or tube 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 interesting examples and apply them to obtain a new Minkowski measurability criterion. We also reflect on the notion of h-Minkowski measurability (where h is an appropriate gauge function), which is connected to the existence of principal complex dimensions of higher order (i.e., multiplicity).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Napomena
Izložio na konferenciji 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