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## Lapidus zeta functions of arbitrary fractals and compact sets in Euclidean spaces

Lapidus, L. Michel; Radunović, Goran; Žubrinić, Darko
Lapidus zeta functions of arbitrary fractals and compact sets in Euclidean spaces // Global qualitative theory of ordinary differential equations and its applications
Research Insitute for Mathematical Sciences (RIMS), Kyoto University, Kyoto, Japan, 2012. (pozvano predavanje, međunarodna recenzija, sažetak, znanstveni)

Naslov
Lapidus zeta functions of arbitrary fractals and compact sets in Euclidean spaces

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

Sažeci sa skupova, sažetak, znanstveni

Skup
Global qualitative theory of ordinary differential equations and its applications

Mjesto i datum
Research Insitute for Mathematical Sciences (RIMS), Kyoto University, Kyoto, Japan, 07.11.2012

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Lapidus zeta functions; distance zeta function; tube zeta function; fractal sets; minkowski content; box dimension; meromorphic function

Sažetak
A new class of zeta functions, for which I propose the name indicated in the title of this talk, has been discovered by Professor Michel L. Lapidus in 2009, during my lecture delivered at a conference at the University of Catania, Italy. The discovery has been disclosed to me immediately after the lecture, and it was a starting point of our joint work. The new zeta functions represent a bridge between the geometry of fractal sets and complex analysis. In this talk I have the privilege of reporting the main results from this paper, some of them obtained very recently. Assume that $A$ is a nonempty, bounded set in $R^N$, and let $d(x, A)$ denote the Euclidean distance from $x\in R^N$ to $A$. Fixing any $\delta>0$, let $A_\delta$ be an open $\d$-neighbourhood of $A$. Then the {;\em Lapidus zeta function}; (in \cite{;LaRaZu}; we call it the {;\em distance zeta function};) is defined as follows: $$\zeta_A(s)=\int_{;A_\delta};d(x, A)^{;s-N};dx.$$ Here $s$ is a complex number, and the integral is understood in the sense of Lebesgue. This zeta function has several remarkable properties. (50 min. lecture delivered by D. Zubrinic)

Izvorni jezik
Engleski

Znanstvena područja
Matematika