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## Relative Zeta Functions of Lapidus Type

Lapidus, Michel L.; Radunović, Goran; Žubrinić, Darko
Relative Zeta Functions of Lapidus Type // Permanent International Session of Research Seminars / Carfi, David (ur.).
Messina, Italija: University of Messina, 2011. str. 28-28 (pozvano predavanje, međunarodna recenzija, sažetak, znanstveni)

Naslov
Relative Zeta Functions of Lapidus Type

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

Sažeci sa skupova, sažetak, znanstveni

Izvornik
Permanent International Session of Research Seminars / Carfi, David - Messina, Italija : University of Messina, 2011, 28-28

Skup
First International Meeting PISRS - PISRS Conference 2011 - Analysis, Fractal Geometry, Dynamical Systems and Economics

Mjesto i datum
Messina, Italija, 08-12.11.2011

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Relative zeta function; fractal set; box dimension; reduced complex dimension; Minkowski content; singular integral

Sažetak
We extend the definition of zeta functions discovered by M.L. Lapidus in Catania 2009 associated to bounded fractal sets which are subsets of the N-­dimensional Euclidean space to the case of unbounded fractal sets with respect to a set of finite Lebesgue measure. For a possibly unbounded set A and Ω a set of finite Lebesgue measure we define the upper d-dimensional Minkowski content of A with respect to Ω. Using that we can define the upper relative box dimension of A with respect to Ω as the infimum of all d for which the upper relative Minkowski content is equal to zero. We show that the relative zeta function of A with respect to Ω is analytic on the half plane for which the real part of the argument is greater or equal to the upper relative box dimension. Moreover, this bound is optimal. We will illustrate the proof and show a few examples. Presented by Goran Radunović.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Napomena