Dimensions of sums with self-similar sets
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.
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arXiv subjects
Daniel Oberlin
Publications and source records attributed to Daniel Oberlin.
Spherical Means and Pinned Distance Sets
We use mixed norm estimates for the spherical averaging operator to obtain some results concerning pinned distance sets.
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Application of a Fourier restriction theorem to certain families of projections in R^3
We use a restriction theorem for Fourier transforms of fractal measures to study projections onto families of planes in R^3 whose normal directions form nondegenerate curves.
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Unit Distance Problems
We study some discrete and continuous variants of the following problem of Erdos: given a finite subset P of R^2 or R^3, what is the maximum number of pairs (p_1,p_2) with p_1,p_2 in P and |p_1 -p_2 |=1?
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Convolution estimates and model surfaces of low codimension
We give examples of measures on certain k-surfaces in R^d. These measures satisfy convolution estimates which are nearly optimal.
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Averages over curves with torsion
We establish $L^p$ Sobolev mapping properties for averages over certain curves in $\R^3$, which improve upon the estimates obtained by $L^2-L^\infty$ interpolation.
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