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$\newcommand{\RR}{\mathbb{R}}$Consider $x\in\RR^n$ and $D\in \RR^{n\times p}$ with $p\geq n$ and full rank. My question is: How many facets can the polytope $ \{x\in\RR^n\ :\ \|D^T x\|_1\leq 1\}$ …

This is also related to equiangular tight frames (ETFs). A frame is a kind of "overcomplete basis" of an inner product space; more precisely a family $(f_1,\dots,f_n)$ of vectors of an inner product s …

To expand Robert Israel's comment: The class of log-nonexpansinve functions on $]0,\infty[$ is the image of the nonexpansive functions of $\mathbb{R}$ under conjugation with $\exp:\mathbb{R}\to ]0,\in …

For complete distance information, this is known as "multidimensional scaling" and heavily used in social sciences or psychology. Actually, there is a very simple approach in this case based on the si …

For the $n$-simplex $$\Delta_n = \{x\in\mathbb{R}^{n+1}\ :\ x_i\geq 0, \sum x_i = 1\},$$ its "midpoint" $m = [1,\dots, 1]/(n+1)$, and its corners $e_k$ it holds that $$\|m - e_k\|\to \infty$$ while …

While the proof in Ball's paper Cube Slicing in $\mathbb{R}^n$ uses probability theory, the result is deterministic. It is proved that the function $f(t) = |(H+ta)\cap Q|$ (where $H$ is the hyperplane …

Probably the paper Fixed Point Properties Related to Multivalued Mappings answers your question...

Changing the tune/pitch of a sound-piece is a scaling/dilation of the Fourier transform. Similarly, zooming of an image is also a scaling/dilation of the (now 2D) Fourier transform. JPEG compression …

Pythagoras' theorem is a special case of the three point identity for Bregman distances: Let $h$ be convex and lower semi-continuous on a Banach space - further assume differentiability of $h$ for sim …