For some self-similar sets $K\subset {\mathbb {R}}^d$ we obtain certain lower bounds for the lower Minkowski dimension of $K+E$ in terms of the lower Minkowski dimension of $E$.
@article{10_4064_cm6683_6_2016,
author = {Daniel Oberlin and Richard Oberlin},
title = {Dimensions of sums with self-similar sets},
journal = {Colloquium Mathematicum},
pages = {43--54},
year = {2017},
volume = {147},
number = {1},
doi = {10.4064/cm6683-6-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm6683-6-2016/}
}
TY - JOUR
AU - Daniel Oberlin
AU - Richard Oberlin
TI - Dimensions of sums with self-similar sets
JO - Colloquium Mathematicum
PY - 2017
SP - 43
EP - 54
VL - 147
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4064/cm6683-6-2016/
DO - 10.4064/cm6683-6-2016
LA - en
ID - 10_4064_cm6683_6_2016
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%A Daniel Oberlin
%A Richard Oberlin
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%J Colloquium Mathematicum
%D 2017
%P 43-54
%V 147
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/cm6683-6-2016/
%R 10.4064/cm6683-6-2016
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Daniel Oberlin; Richard Oberlin. Dimensions of sums with self-similar sets. Colloquium Mathematicum, Tome 147 (2017) no. 1, pp. 43-54. doi: 10.4064/cm6683-6-2016