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Homogeneous kernels and self similar sets
Indiana University Mathematics Journal, 2015 We consider singular integrals associated to homogeneous kernels on self similar sets. Using ideas from ergodic theory we prove, among other things, that in Euclidean spaces the principal values of singular integrals associated to real analytic, homogeneous kernels fail to exist a.e.
Chousionis, Vasilis, Urbański, Mariusz
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Self-Similar Sets: Projections, Sections and Percolation [PDF]
, 2017 We survey some recent results on the dimension of orthogonal projections of self-similar sets and of random subsets obtained by percolation on self-similar sets. In particular we highlight conditions when the dimension of the projections takes the generic value for all, or very nearly all, projections. We then describe a method for deriving dimensional
Falconer, Kenneth John, Jin, Xiong
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p-energies on p.c.f. self-similar sets
Advances in Mathematics, 2022 We study $p$-energies on post critically finite (p.c.f.) self-similar sets for ...
Cao, Shiping, Gu, Qingsong, Qiu, Hua
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Arithmetic on self-similar sets [PDF]
Indagationes Mathematicae, 2020 Let $K_1$ and $K_2$ be two one-dimensional homogeneous self-similar sets. Let $f$ be a continuous function defined on an open set $U\subset \mathbb{R}^{2}$. Denote the continuous image of $f$ by $$ f_{U}(K_1,K_2)=\{f(x,y):(x,y)\in (K_1\times K_2)\cap U\}.
Zhao, Bing +3 more
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, 2022 Diabetes mellitus (DM) has become a global health problem because the prevalence of diabetes mellitus continues to increase. Data from the West Sumatra Provincial Health Office (2018), DM cases totalled 44,280 cases, with a DM prevalence of 1.6% in 2018.
Marlinda, Roza +4 more
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Publicationes Mathematicae Debrecen, 2022 To appear in Publ.
Jia, Qi, Li, Yuanyuan, Jiang, Kan
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Self-similar sets in convex metric spaces
Journal of Numerical Analysis and Approximation Theory, 2004 The purpose of this paper is to present some existence and uniqueness results for self-similar sets in convex complete metric spaces.
Ghiocel Moţ
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Lacunarity of self-similar and stochastically self-similar sets [PDF]
Transactions of the American Mathematical Society, 1999 Let K K be a self-similar set in
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On the distance sets of self-similar sets
Nonlinearity, 2012 13 pages, one figure; exposition clarified and typos corrected in v2; to appear in ...
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Computing the Hessenberg matrix associated with a self-similar measure
, 2011 We introduce in this paper a method to calculate the Hessenberg matrix of a sum of measures from the Hessenberg matrices of the component measures. Our method extends the spectral techniques used by G.
Torrano, E. +7 more
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