Now showing items 1-6 of 6

    • Average distances on self-similar sets and higher order average distances of self-similar measures 

      Allen, D.; Edwards, H.; Harper, S.; Olsen, Lars Ole Ronnow (2017-10) - Journal article
      The purpose of this paper is twofold: (1) We study different notions of the average distance between two points of a self-similar subset of ℝ, and (2) we investigate the asymptotic behaviour of higher order average moments ...
    • Mixed moments and local dimensions of measures 

      Olsen, Lars Ole Ronnow (2016-09-01) - Journal article
      We analyse the asymptotic behaviour of the mixed moments of Borel probability measures on [0,1]d. In particular, we prove that the asymptotic behaviour of the mixed moments of a measure is intimately related to the local ...
    • Multifractal spectra and multifractal zeta-functions 

      Mijovic, Vuksan; Olsen, Lars Ole Ronnow (2017-02) - Journal article
      We introduce multifractal zetafunctions providing precise information of a very general class of multifractal spectra, including, for example, the multifractal spectra of self-conformal measures and the multifractal spectra ...
    • On simultaneous local dimension functions of subsets of Rd 

      Olsen, Lars Ole Ronnow (2015-09-30) - Journal article
      For a subset E ⊑ Rd and x ∈ Rd, the local Hausdorff dimension function of E at x and the local packing dimension function of E at x are defined by (Formula presented.) where dimH and dimP denote the Hausdorff dimension and ...
    • On the rate of convergence of ((||ƒ||p)¦(||ƒ||∞))p as p →∞ 

      Olsen, Lars Ole Ronnow (2019-02) - Journal article
      Let (X,ε,μ) be a measure space and let ƒ:X→ ℝ be a measurable function such that ||ƒ||p < ∞ for all p ≥ 1 and ||ƒ||∞ >0.  In this paper, we describe the rate of convergence of ((||ƒ||p)¦(||ƒ||∞))p as p →∞.
    • On the Π^0_γ-completeness and Σ^0_γ-completeness of multifractal decomposition sets 

      Olsen, Lars Ole Ronnow (2018) - Journal article
      The purpose of this paper twofold. Firstly, we establish Π^0_γ-completeness and Σ^0_γ-completeness of several different classes of multifractal decomposition sets of arbitrary Borel measures (satisfying a mild non-degeneracy ...