Fractal tube formulas for compact sets and relative fractal drums: oscillations, complex dimensions and fractality

DOI10.4171/JFG/57zbMath1426.11084arXiv1604.08014WikidataQ113999188 ScholiaQ113999188MaRDI QIDQ1708550

Darko Žubrinić, Michel L. Lapidus, Goran Radunović

Publication date: 23 March 2018

Published in: Journal of Fractal Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.08014

zbMATH Keywords

Mellin transformbox dimensionfractal setdistance zeta functionfractal stringMinkowski measurable settube zeta functionfractal tube formulafractal zeta functionrelative fractal drum

Mathematics Subject Classification ID

Contents, measures, outer measures, capacities (28A12) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Other Dirichlet series and zeta functions (11M41) Fractals (28A80) Convergence and divergence of integrals (40A10) General integral transforms (44A05)

Related Items (9)

Complex dimensions of fractals and meromorphic extensions of fractal zeta functions ⋮ Fractal zeta functions of orbits of parabolic diffeomorphisms ⋮ \(h\)-Laplacians on singular sets ⋮ Quasiperiodic sets at infinity and meromorphic extensions of their fractal zeta functions ⋮ Fractal codimension of nilpotent contact points in two-dimensional slow-fast systems ⋮ Fractal tube formulas and a Minkowski measurability criterion for compact subsets of Euclidean spaces ⋮ Distance and tube zeta functions of fractals and arbitrary compact sets ⋮ Fractal Zeta Functions and Complex Dimensions: A General Higher-Dimensional Theory ⋮ An overview of complex fractal dimensions: from fractal strings to fractal drums, and back

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