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Fractal tube formulas for relative fractal drums in arbitrary Euclidean spaces via Lapidus zeta functions (CROSBI ID 631377)

Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija

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. et al. (ur.). Providence (RI): American Mathematical Society (AMS), 2016. str. 128-129

Podaci o odgovornosti

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

engleski

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

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).

fractal tube formula; relative fractal drum; fractal zeta function; Minkowski measurability

Izložio na konferenciji Goran Radunović

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Podaci o prilogu

128-129.

2016.

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objavljeno

Podaci o matičnoj publikaciji

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): American Mathematical Society (AMS)

0192-5857

Podaci o skupu

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

pozvano predavanje

06.01.2016-09.01.2016

Seattle (WA), Sjedinjene Američke Države

Povezanost rada

Matematika