Publications (24)
On Bisectors in Normed Spaces
Thomas Jahn, Margarita Spirova
In this note, we completely describe the shape of the bisector of two given points in a two-dimensional normed vector space. More precisely, we show that, depending on the position…
Is a complete, reduced set necessarily of constant width?
René Brandenberg, Bernardo González Merino, Thomas Jahn +1
Is it true that a convex body being complete and reduced with respect to some gauge body is necessarily of constant width, that is, satisfies for some ?…
Successive Radii and Ball Operators in Generalized Minkowski Spaces
Thomas Jahn
We investigate elementary properties of successive radii in generalized Minkowski spaces (that is, with respect to gauges), i.e., we measure the "size" of a given convex set in a f…
Coproximinality of linear subspaces in generalized Minkowski spaces
Thomas Jahn, Christian Richter
We show that, for vector spaces in which distance measurement is performed using a gauge, the existence of best coapproximations in -codimensional closed linear subspaces implie…
Universal approximation with complex-valued deep narrow neural networks
Paul Geuchen, Thomas Jahn, Hannes Matt
We study the universality of complex-valued neural networks with bounded widths and arbitrary depths. Under mild assumptions, we give a full description of those activation functio…
Geometric Algorithms for Minimal Enclosing Discs in Strictly Convex Normed Planes
Thomas Jahn
With the geometric background provided by Alonso, Martini, and Spirova on the location of circumcenters of triangles in normed planes, we show the validity of the Elzinga--Hearn al…
On the optimal constants in the two-sided Stechkin inequalities
Thomas Jahn, Tino Ullrich
We address the optimal constants in the strong and the weak Stechkin inequalities, both in their discrete and continuous variants. These inequalities appear in the characterization…
Ball Convex Bodies in Minkowski Spaces
Thomas Jahn, Christian Richter, Horst Martini
The notion of ball convexity, considered in finite dimensional real Banach spaces, is a natural and useful extension of usual convexity; one replaces intersections of half-spaces b…
Phases of spin- and mass-imbalanced ultracold Fermi gases in harmonic traps
Jens Braun, JoaquÃn E. Drut, Thomas Jahn +2
We analyze the phase structure of mass- and spin-imbalanced unitary Fermi gases in harmonic traps. To this end, we employ Density Functional Theory in the local density approximati…
Sampling numbers of smoothness classes via -minimization
Thomas Jahn, Tino Ullrich, Felix Voigtlaender
Using techniques developed recently in the field of compressed sensing we prove new upper bounds for general (nonlinear) sampling numbers of (quasi-)Banach smoothness spaces in $L^…
Vertex-Facet Assignments For Polytopes
Thomas Jahn, Martin Winter
Motivated by the search for reduced polytopes, we consider the following question: For which polytopes exists a vertex-facet assignment, that is, a matching between vertices and no…
The HETDEX Instrumentation: Hobby-Eberly Telescope Wide Field Upgrade and VIRUS
Gary J. Hill, Hanshin Lee, Phillip J. MacQueen +46
The Hobby-Eberly Telescope (HET) Dark Energy Experiment (HETDEX) is undertaking a blind wide-field low-resolution spectroscopic survey of 540 square degrees of sky to identify and…
Stability of Constrained Adaptive Model Predictive Control Algorithms
Thomas Jahn, Jürgen Pannek
Recently, suboptimality estimates for model predictive controllers (MPC) have been derived for the case without additional stabilizing endpoint constraints or a Lyapunov function t…
Minsum Location Extended to Gauges and to Convex Sets
Thomas Jahn, Yaakov S. Kupitz, Horst Martini +1
One of the oldest and richest problems from continuous location science is the famous Fermat-Torricelli problem, asking for the unique point in Euclidean space that has minimal dis…
Uniqueness of circumcenters in generalized Minkowski spaces
Bernardo González Merino, Thomas Jahn, Christian Richter
In an -dimensional normed space every bounded set has a unique circumball if and only if every set of cardinality two has a unique circumball and if and only if the unit ball of…
Orthogonality in Generalized Minkowski Spaces
Thomas Jahn
We combine functional analytic and geometric viewpoints on approximate Birkhoff and isosceles orthogonality in generalized Minkowski spaces which are finite-dimensional vector spac…
Extremal Radii, Diameter, and Minimum Width in Generalized Minkowski Spaces
Thomas Jahn
We discuss the notions of circumradius, inradius, diameter, and minimum width in generalized Minkowski spaces (that is, with respect to gauges), i.e., we measure the "size" of a gi…
Hunting for reduced polytopes
Bernardo González Merino, Thomas Jahn, Alexandr Polyanskii +1
We show that there exist reduced polytopes in three-dimensional Euclidean space. This partially answers the question posed by Lassak on the existence of reduced polytopes in -di…
The ERA2 facility: towards application of a fiber-based astronomical spectrograph for imaging spectroscopy in life sciences
Martin M. Roth, Karl Zenichowski, Nicolae Tarcea +13
Astronomical instrumentation is most of the time faced with challenging requirements in terms of sensitivity, stability, complexity, etc., and therefore leads to high performance d…
Hunting for reduced polytopes
Bernardo González Merino, Thomas Jahn, Gerd Wachsmuth
By correcting an example by Polyanskii, we show that there exist reduced polytopes in three-dimensional Euclidean space. This partially answers the question posed by Lassak on the…
Tate Conjecture and Higher Brauer Groups of Abelian Varieties in Characteristic Zero
Thomas Jahn
Let be an abelian variety over a field finitely generated over . We show that the finiteness of the -primary torsion subgroup of the higher Brauer group is a…
Besov regularity of random wavelet series
Andreas Horst, Thomas Jahn, Felix Voigtlaender
We study the Besov regularity of wavelet series on with randomly chosen coefficients. More precisely, each coefficient is a product of a random factor and a paramete…
Minkowski chirality: a measure of reflectional asymmetry of convex bodies
Andrei Caragea, Katherina von Dichter, Kurt Klement Gottwald +3
Using an optimal containment approach, we quantify the asymmetry of convex bodies in with respect to reflections across affine subspaces of a given dimension. We pro…
Marcinkiewicz--Zygmund inequalities for scattered and random data on the -sphere
Frank Filbir, Ralf Hielscher, Thomas Jahn +1
The recovery of multivariate functions and estimating their integrals from finitely many samples is one of the central tasks in modern approximation theory. Marcinkiewicz--Zygmund…