Related papers: Intermediate dimensions under self-affine codings
We consider the problem of bounding the number of exceptional projections (projections which are smaller than typical) of a subset of a vector space over a finite field onto subspaces. We establish bounds that depend on $L^p$ estimates for…
We develop quantitative algorithmic information bounds for orthogonal projections and distances in the plane. Under mild independence conditions, the distance $|x-y|$ and a projection coordinate $p_e x$ each retain at least half the…
Around 1930, K. Menger expressed his interest in the concept of abstract angle function. He introduced a general definition of this notion for metric and semi-metric spaces. He also proposed two problems concerning conformal embeddability…
Motivated by recent results on radial projections and applications to the celebrated Falconer distance problem, we study radial projections in the setting of finite fields. More precisely, we extend results due to Mattila and Orponen…
We consider operator scaling $\alpha$-stable random sheets, which were introduced in [12]. The idea behind such fields is to combine the properties of operator scaling $\alpha$-stable random fields introduced in [6] and fractional Brownian…
We develop a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS. In the one dimensional case, our methods require only C^3 regularity of the maps in the IFS. The key idea,…
We investigate graph-directed iterated function systems in mixed Euclidean and p-adic spaces. Hausdorff measure and Hausdorff dimension in such spaces are defined, and an upper bound for the Hausdorff dimension is obtained. The relation…
By using the metric projection onto a closed self-dual cone of the Euclidean space, M. S. Gowda, R. Sznajder and J. Tao have defined generalized lattice operations, which in the particular case of the nonnegative orthant of a Cartesian…
Conformal Galilei Algebras labeled by $d,\ell$ (where $d$ is the number of space dimensions and $\ell$ denotes a spin-${\ell}$ representation w.r.t. the $\mathfrak{sl}(2)$ subalgebra) admit two types of central extensions, the ordinary one…
We consider the method of alternating (metric) projections for pairs of linear subspaces of finite dimensional Banach spaces. We investigate the size of the set of points for which this method converges to the metric projection onto the…
In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson coordinates in [Gillette et al., AiCM, doi:10.1007/s10444-011-9218-z], we prove interpolation error estimates for the mean value coordinates on convex polygons…
This paper is about conic intrinsic volumes and their associated integral geometry. We pay special attention to the biconic localizations of the conic intrinsic volumes, the so-called support measures. An analysis of these quantities has so…
We prove large (and moderate) deviations for a class of linear combinations of spacings generated by i.i.d. exponentially distributed random variables. We allow a wide class of coefficients which can be expressed in terms of continuous…
Suppose $\mu, \nu$ are compactly supported Radon measures on $\mathbb{R}^d$ and $V\in G(d,n)$ is an $n$-dimensional subspace. In this paper we systematically study the mixed-norm $$\int\|\pi^y\mu\|_{L^p(G(d,n))}^q\,d\nu(y),\…
In the context of general iterated function systems (IFSs), we introduce bilinear fractal interpolants as the fixed points of certain Read-Bajraktarevi\'{c} operators. By exhibiting a generalized "taxi-cab" metric, we show that the graph of…
In this paper we consider affine iterated function systems in locally compact non-Archimedean field $\mathbb{F}$. We establish the theory of singular value composition in $\mathbb{F}$ and compute box and Hausdorff dimension of self-affine…
If a real-valued function is continuous on a real interval and it takes on two different values, then it will also take any value in between those two, by the Intermediate Value Theorem. It is not immediately clear what would be a natural…
The parameterisation of rotations in three dimensional Euclidean space is an area of applied mathematics that has long been studied, dating back to the original works of Euler in the 18th century. As such, many ways of parameterising a…
Orthogonal projections onto closed subspaces of $H^2(\mathbb{D}^n)$ of the form $\varphi H^2(\mathbb{D}^n)$ for inner functions $\varphi$ on $\mathbb{D}^n$ are referred to as inner projections, where $H^2(\mathbb{D}^n)$ denotes the Hardy…
We consider the numerical evaluation of one dimensional projections of general multivariate stable densities introduced by Abdul-Hamid and Nolan (1998). In their approach higher order derivatives of one dimensional densities are used, which…