3 citations · 5 across the 6 of their papers we have counts for
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Applications of dimension interpolation to orthogonal projections
Jonathan M. Fraser
Dimension interpolation is a novel programme of research which attempts to unify the study of fractal dimension by considering various spectra which live in between well-studied no…
Assouad dimension and fractal geometry
Jonathan M. Fraser
This is a book to be published in 2020 by Cambridge University Press (Tracts in Mathematics Series). It focuses on the Assouad dimension of sets and measures in Euclidean space, as…
Schmidt's game on Hausdorff metric and function spaces: generic dimension of sets and images
Ábel Farkas, Jonathan M. Fraser, Erez Nesharim +1
We consider Schmidt's game on the space of compact subsets of a given metric space equipped with the Hausdorff metric, and the space of continuous functions equipped with the supre…
Approximate arithmetic structure in large sets of integers
Jonathan M. Fraser, Han Yu
We prove that if a set is `large' in the sense of Erdős, then it approximates arbitrarily long arithmetic progressions in a strong quantitative sense. More specifically, expressing…
Interpolating between dimensions
Jonathan M. Fraser
Dimension theory lies at the heart of fractal geometry and concerns the rigorous quantification of how large a subset of a metric space is. There are many notions of dimension to c…
Intermediate dimensions
Kenneth J. Falconer, Jonathan M. Fraser, Tom Kempton
We introduce a continuum of dimensions which are `intermediate' between the familiar Hausdorff and box dimensions. This is done by restricting the families of allowable covers in t…