Weighted $L^p(\mathbb{R}^n) \to L^q(\mathbb{R}^n)$ Fourier inequalities are studied. We prove Pitt-Boas type results on integrability with power weights of the Fourier transform of a radial function.

We are concerned with the existence and uniqueness of solutions with only bounded density for the barotropic compressible Navier-Stokes equations. Assuming that the initial velocity has slightly sub-critical regularity and ...

The Weyl group of the Cuntz algebra $\mathcal{O}_n$ is investigated. This is (isomorphic to) the group of polynomial automorphisms $\lambda_u$ of $\mathcal{O}_n$, namely those induced by unitaries u that can be written ...

This Snapshot is about the generalization of ">" from ordinary numbers to so-called fields. At the end, I will touch on some ideas in recent research.

Angenommen, eine Gruppe von Einzelpersonen möchte unter verschiedenen Optionen wählen, zum Beispiel einen von mehreren Kandidaten für ein politisches Amt oder den besten Teilnehmer einer Eiskunstlaufmeisterschaft. Man ...

The Willmore problem studies which torus has the least amount of bending energy. We explain how to think of a torus as a donut-shaped surface and how the intuitive notion of bending has been studied by mathematics over time.

In this paper we present a new algorithm for solving the symmetric matrix eigenvalue problem that works by first using a Cayley transformation to convert the symmetric matrix into a unitary one and then uses Gragg’s ...

This snapshot is about zero-dimensional symmetry. Thanks to recent discoveries we now understand such symmetry better than previously imagined possible. While still far from complete, a picture of zero-dimensional symmetry ...

Die Yang–Baxter-Gleichung ist eine faszinierende Gleichung, die in vielen Gebieten der Physik und der Mathematik auftritt und die am besten diagrammatisch dargestellt wird. Dieser Snapshot schlägt einen weiten Bogen ...