Webproperties of the harmonic measure, u, of plane DLA. The need for two distinct scal- ings implies that the notion of self-similarity splits into several distinct sub-notions. Our more significant new scaling property of is unusual, and indicates that DLA satisfies an "extended form" of self-similarity, but not the form that is ordinarily pos- WebIn Chapter IV we introduce measure to this theory. Self-similar group is a rather new notion in geometric group theory. Like the self-similar objects in geometry (fractals) are too irregular to be described using the language of classical Euclidean geometry, the self-similar groups possess properties not typical for the traditional group theory.
Self-Similarity -- from Wolfram MathWorld
WebSelf-similar measures and harmonic analysis. This is a survey of some recent work on the spectral properties and the Fourier asymptotics of self-similar measures defined on . … WebNov 4, 2024 · The purpose of the present paper is to prove new results for certain stochastic processes which arise from self-similar fractals. We accomplish this by making a number of new links between following two settings: (i) the harmonic analysis of the ∇ μ operators for general positive non-atomic Borel measures, and (ii) more standard harmonic analysis … staytonrx wvi.com
Fractals in Probability and Analysis
WebMar 24, 2024 · Self-Similarity. An object is said to be self-similar if it looks "roughly" the same on any scale. Fractals are a particularly interesting class of self-similar objects. Self … WebI am interested in harmonic analysis and geometric measure theory. Xi'an, Shaanxi, China . The University of Wisconsin-Madison: Department of Mathematics: 480 Lincoln Drive: Madison, WI 53706 : WebA wide range of related topics are discussed, including self-similar measures and distributions, fractal Plancherel theorems, L p dimensions and densities of measures, … stayton weather