# Dimensions of sums with self-similar sets

@article{Oberlin2015DimensionsOS,
title={Dimensions of sums with self-similar sets},
author={Daniel Oberlin and Richard Oberlin},
journal={arXiv: Classical Analysis and ODEs},
year={2015}
}
• Published 23 June 2015
• Mathematics
• arXiv: Classical Analysis and ODEs
For some self-similar sets K in d-dimensional Euclidean space we obtain certain lower bounds for the lower Minkowski dimension of K+E in terms of the lower Minkowski dimension of E.
2 Citations
• Mathematics
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A compact set E⊂Rd is said to be arithmetically thick if there exists a positive integer n so that the n ‐fold arithmetic sum of E has non‐empty interior. We prove the arithmetic thickness of E , if
• Mathematics
• 2020
A compact set $E\subset {\Bbb R}^d$ is said to be arithmetically thick if there exists a positive integer $n$ so that the $n$-fold arithmetic sum of $E$ has non-empty interior. We prove the

## References

SHOWING 1-9 OF 9 REFERENCES

We study lower bounds for the Minkowski and Hausdorff dimensions of the algebraic sum E+K of two sets E,K⊂ℝd.
AbstractWe prove inequalities which give lower bounds for the Lebesgue measures of setsE +K whereK is a certain kind of Cantor set. For example, ifC is the Cantor middle-thirds subset of the circle
• Mathematics
Ergodic Theory and Dynamical Systems
• 1997
We find conditions on the ratios of dissection of a Cantor set so that the group it generates under addition has positive Lebesgue measure. In particular, we answer affirmatively a special case of a
• Mathematics
Ergodic Theory and Dynamical Systems
• 2009
Abstract Let Ca be the central Cantor set obtained by removing a central interval of length 1−2a from the unit interval, and then continuing this process inductively on each of the remaining two
• Mathematics
• 2007
The circle method is introduced, which is a nice application of Fourier analytic techniques to additive problems and its other applications: Vinogradov without GRH, partitions, Waring’s problem.
• Mathematics
• 2009
Let A be a subset of the real line. We study the fractal dimensions of the k-fold iterated sumsets kA, defined as $$kA =\{ {a}_{1} + \cdots + {a}_{k} : {a}_{i} \in A\}.$$ We show that for any