Zeta functions and complex dimensions of relative fractal drums: theory, examples and applications

DOI10.4064/DM757-4-2017zbMath1406.11092arXiv1603.00946OpenAlexW3101130161WikidataQ113999242 ScholiaQ113999242MaRDI QIDQ3130499

Michel L. Lapidus, Goran Radunović, Darko Žubrinić

Publication date: 22 January 2018

Published in: Dissertationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.00946

zbMATH Keywords

fractal setrelative fractal drumfractal zeta functionsholomorphic and meromorphic functionsa-string of higher orderrelative Minkowski contentrelative Minkowski measurabilitytranscendentally quasiperiodic function

Mathematics Subject Classification ID

Contents, measures, outer measures, capacities (28A12) Other Dirichlet series and zeta functions (11M41) Length, area, volume, other geometric measure theory (28A75) Fractals (28A80) Meromorphic functions of one complex variable (general theory) (30D30) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

Related Items (7)

Fractal zeta functions of orbits of parabolic diffeomorphisms ⋮ Quasiperiodic sets at infinity and meromorphic extensions of their fractal zeta functions ⋮ Fractal tube formulas and a Minkowski measurability criterion for compact subsets of Euclidean spaces ⋮ Fractal zeta functions and complex dimensions of relative fractal drums ⋮ Fractal Zeta Functions and Complex Dimensions: A General Higher-Dimensional Theory ⋮ Regularly varying functions, generalized contents, and the spectrum of fractal strings ⋮ An overview of complex fractal dimensions: from fractal strings to fractal drums, and back

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