19 citations · 74 across the 11 of their papers we have counts for
8 papers · 1 filter
Essential singularities of fractal zeta functions
Michel L. Lapidus, Goran Radunović, Darko Žubrinić
We study the essential singularities of geometric zeta functions , associated with bounded fractal strings . For any three prescribed real numbers $D_{\…
Minkowski measurability criteria for compact sets and relative fractal drums in Euclidean spaces
Michel L. Lapidus, Goran Radunović, Darko Žubrinić
We establish a Minkowski measurability criterion for a large class of relative fractal drums (or, in short, RFDs), in Euclidean spaces of arbitrary dimension in terms of their comp…
Fractal Tube Formulas for Compact Sets and Relative Fractal Drums: Oscillations, Complex Dimensions and Fractality
Michel L. Lapidus, Goran Radunović, Darko Žubrinić
We establish pointwise and distributional fractal tube formulas for a large class of relative fractal drums in Euclidean spaces of arbitrary dimensions. A relative fractal drum (or…
Zeta Functions and Complex Dimensions of Relative Fractal Drums: Theory, Examples and Applications
Michel L. Lapidus, Goran Radunović, Darko Žubrinić
In 2009, the first author introduced a new class of zeta functions, called `distance zeta functions', associated with arbitrary compact fractal subsets of Euclidean spaces of arbit…
Fractality and Lapidus zeta functions at infinity
Goran Radunović
We study fractality of unbounded sets of finite Lebesgue measure at infinity by introducing the notions of Minkowski dimension and content at infinity. We also introduce the Lapidu…
Complex dimensions of fractals and meromorphic extensions of fractal zeta functions
Michel L. Lapidus, Goran Radunović, Darko Žubrinić
We study meromorphic extensions of distance and tube zeta functions, as well as of geometric zeta functions of fractal strings. The distance zeta function $ζ_A(s):=\int_{A_δ} d(x,A…
Distance and tube zeta functions of fractals and arbitrary compact sets
Michel L. Lapidus, Goran Radunović, Darko Žubrinić
Recently, the first author has extended the definition of the zeta function associated with fractal strings to arbitrary bounded subsets of the -dimensional Euclidean space…
Fractal tube formulas and a Minkowski measurability criterion for compact subsets of Euclidean spaces
Michel L. Lapidus, Goran Radunović, Darko Žubrinić
We establish pointwise and distributional fractal tube formulas for a large class of compact subsets of Euclidean spaces of arbitrary dimensions. These formulas are expressed as su…