The spectral dimension of a fractal Laplacian encodes important geometric, analytic, and measure-theoretic information. Unlike standard Laplacians on Euclidean spaces or Riemannian manifolds, the spectral dimension of...
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The spectral dimension of a fractal Laplacian encodes important geometric, analytic, and measure-theoretic information. Unlike standard Laplacians on Euclidean spaces or Riemannian manifolds, the spectral dimension of fractal Laplacians are often non-integral and difficult to compute. The computation is much harder in higher-dimensions. In this paper, we set up a framework for computing the spectral dimension of the Laplacians defined by a class of graph-directed self-similar measures on R-d (d >= 2) satisfying the graph open set condition. The main ingredients of this framework include a technique of Naimark and Solomyak and a vector-valued renewal theorem of Lau et al.
We consider the graph-directed iterated function systems and give upper bounds for the diameters of the smallest disks enclosing their attractors. We also give an algorithm to obtain these smallest enclosing disks wit...
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We consider the graph-directed iterated function systems and give upper bounds for the diameters of the smallest disks enclosing their attractors. We also give an algorithm to obtain these smallest enclosing disks with any proximity. (C) 2018 Elsevier Ltd. All rights reserved.
Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the iteratedfunctionsystem (IFS) corresponding to a data set is the graph of the...
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Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the iteratedfunctionsystem (IFS) corresponding to a data set is the graph of the FIF. Coalescence Hidden-variable Fractal Interpolation function (CHFIF) is both self-affine and non self-affine in nature depending on the free variables and constrained free variables for a generalized IFS. In this article, graphdirectediteratedfunctionsystem for a finite number of generalized data sets is considered and it is shown that the projection of the attractors on is the graph of the CHFIFs interpolating the corresponding data sets.
Using Tukia's method for representing a quasisymmetric function as a quasisymmetric sieve, we generalize his modification to the Salem scheme and find a sufficient condition for the collection of functions that re...
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Using Tukia's method for representing a quasisymmetric function as a quasisymmetric sieve, we generalize his modification to the Salem scheme and find a sufficient condition for the collection of functions that realize a structure parametrization of a graph-directedfunctionsystem of a particular form (a one-dimensional multizipper) to consist of quasisymmetric functions. We give an asymptotically sharp estimate for the quasisymmetry coefficient of these functions in terms of the dilation coefficients of the mappings constituting a given multizipper, which yields a substantially more general method for constructing quasisymmetric functions than Tukia's construction.
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