During the past two decades there has been active interplay between geometric measure
theory and Fourier analysis. This book describes part of that development, concentrating on …

We study the dimension of self-similar sets and measures on the line. We show that if the
dimension is less than the generic bound of min {1, s}, where s is the similarity dimension …

This is a mathematically rigorous introduction to fractals which emphasizes examples and
fundamental ideas. Building up from basic techniques of geometric measure theory and …

On Falconer’s distance set problem in the plane | Inventiones mathematicae Skip to main
content Springer Nature Link Account Menu Find a journal Publish with us Track your research …

We study a class of measures on the real line with a kind of self-similar structure, which we
call dynamically driven self-similar measures, and contain proper self-similar measures such …

The Bernoulli convolution with parameter λ∈(0, 1) is the measure on R that is the
distribution of the random power series∑±λn, where±are independent fair cointosses. This …

The distribution VA of the random series L:±. xn is the infinite convolution product of~(LAn+
DAn). These measures have been studied since the 1930's, revealing connections with …

We fully resolve the Furstenberg set conjecture in $\mathbb {R}^ 2$, that a $(s, t) $-
Furstenberg set has Hausdorff dimension $\ge\min (s+ t,\frac {3s+ t}{2}, s+ 1) $. As a result …

When does a Bernoulli convolution admit a spectrum? - ScienceDirect Skip to main contentSkip
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We study the Erdös/Falconer distance problem in vector spaces over finite fields. Let
${\mathbb F} _q $ be a finite field with $ q $ elements and take $ E\subset {\mathbb F}^ d_q …