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}
}
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. 

On arithmetic sums of fractal sets in Rd

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

On arithmetic sums of fractal sets in ${\Bbb R}^d$

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

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E-mail address: roberlin@math.fsu.edu

  • E-mail address: roberlin@math.fsu.edu

E-mail address: oberlin@math.fsu.edu

  • E-mail address: oberlin@math.fsu.edu