Relative Zeta Functions of Lapidus Type (CROSBI ID 584546)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija
Podaci o odgovornosti
Lapidus, Michel L. ; Radunović, Goran ; Žubrinić, Darko
engleski
Relative Zeta Functions of Lapidus Type
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.
relative zeta function; fractal set; box dimension; reduced complex dimension; Minkowski content; singular integral
Izložio na konferenciji Goran Radunović.
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Podaci o prilogu
28-28.
2011.
objavljeno
Podaci o matičnoj publikaciji
Permanent International Session of Research Seminars
Carfi, David
Messina: University of Messina
Podaci o skupu
First International Meeting PISRS - PISRS Conference 2011 - Analysis, Fractal Geometry, Dynamical Systems and Economics
pozvano predavanje
08.11.2011-12.11.2011
Messina, Italija