Tube formulas and complex dimensions of self-similar tilings

DOI10.1007/s10440-010-9562-xzbMath1244.28013arXivmath/0605527OpenAlexW2093660071MaRDI QIDQ708842

Michel L. Lapidus, Erin P. J. Pearse

Publication date: 14 October 2010

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605527

zbMATH Keywords

zeta functionsinradiuscomplex dimensionsfractal stringself-similar tilingtube formulacurvature matrixdistributional explicit formulafractal Steiner formulagenerating function for the geometry

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Contents, measures, outer measures, capacities (28A12) (zeta (s)) and (L(s, chi)) (11M06) Length, area, volume, other geometric measure theory (28A75) Fractals (28A80)

Related Items (18)

Inner tube formulas for polytopes ⋮ Minkowski content and fractal curvatures of self-similar tilings and generator formulas for self-similar sets ⋮ Lattice-type self-similar sets with pluriphase generators fail to be Minkowski measurable ⋮ Tube formulas for self-similar and graph-directed fractals ⋮ Scaling exponents of curvature measures ⋮ Towards quantized number theory: spectral operators and an asymmetric criterion for the Riemann hypothesis ⋮ Truncated infinitesimal shifts, spectral operators and quantized universality of the Riemann zeta function ⋮ Fractal tube formulas and a Minkowski measurability criterion for compact subsets of Euclidean spaces ⋮ Book review of: M. Lapidus et al., Fractal zeta functions and fractal drums. Higher-dimensional theory of complex dimensions ⋮ Distance and tube zeta functions of fractals and arbitrary compact sets ⋮ Multifractal spectra and multifractal zeta-functions ⋮ Geometry of canonical self-similar tilings ⋮ Fractal zeta functions and complex dimensions of relative fractal drums ⋮ Self-similar \(p\)-adic fractal strings and their complex dimensions ⋮ Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators ⋮ 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 ⋮ Tube volumes via functional equations

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