Self-Similar Measures
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چکیده
منابع مشابه
Exact dimensionality and projections of random self-similar measures and sets
We study the geometric properties of random multiplicative cascade measures defined on self-similar sets. We show that such measures and their projections and sections are almost surely exact-dimensional, generalizing Feng and Hu’s result [10] for self-similar measures. This, together with a compact group extension argument, enables us to generalize Hochman and Shmerkin’s theorems on projection...
متن کاملLarge Scale Renormalisation of Fourier Transforms of Self-similar Measures and Self-similarity of Riesz Measures
We shall show that the oscillations observed by Strichartz JRS92, Str90] in the Fourier transforms of self-similar measures have a large-scale renormali-sation given by a Riesz-measure. Vice versa the Riesz measure itself will be shown to be self-similar around every triadic point.
متن کاملSelf-similar Random Fractal Measures Using Contraction Method in Probabilistic Metric Spaces
Self-similar random fractal measures were studied by Hutchinson and Rüschendorf. Working with probability metric in complete metric spaces, they need the first moment condition for the existence and uniqueness of these measures. In this paper, we use contraction method in probabilistic metric spaces to prove the existence and uniqueness of self-similar random fractal measures replacing the firs...
متن کاملComputing the Hessenberg matrix associated with a self-similar measure
We introduce in this paper a method to calcúlate 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. Mantica to calcúlate the Jacobi matrix associated with a sum of measures from the Jacobi matrices of each of the measures. We apply this method to approximate the Hessenberg matrix associated wit...
متن کاملSelf-similar Measures Associated with Ifs with Non-uniform Contraction Ratios
In this paper we study the absolute continuity of self-similar measures defined by iterated function systems (IFS) whose contraction ratios are not uniform. We introduce a transversality condition for a multi-parameter family of IFS and study the absolute continuity of the corresponding self-similar measures. Our study is a natural extension of the study of Bernoulli convolutions by Solomyak, P...
متن کاملSelf-similar Measures Associated to Ifs with Non-uniform Contraction Ratios
In this paper we study the absolute continuity of self-similar measures defined by iterated function systems (IFS) whose contraction ratios are not uniform. We introduce a transversality condition for a multi-parameter family of IFS and study the absolute continuity of the corresponding self-similar measures. Our study is a natural extension of the study of Bernoulli convolutions by Solomyak, P...
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تاریخ انتشار 2007