Related papers: On 2-dimensional mobile sampling

We establish a regular sampling theory in the range of the analysis operator of a continuous frame having a unitary structure. The unitary structure is related with a unitary representation of a locally compact abelian group on a separable…

This paper investigates the existence and properties of stable, uniformly rotating star-planet systems, i.e. mass ratio is sufficiently small. It is modeled by the Euler-Poisson equations. Following the framework established by McCann for…

We show that if $1<p\neq 2<\infty$, then any isometry of the $p$-convexification of the combinatorial Banach space associated with a hereditary family of finite subsets of $\mathbb{N}$ containing the singletons is given by a signed…

A weighted area estimate for entire graphs with bounded weighted mean curvature in Gauss space is given by a simple proof. Bernstein type theorems for self shrinkers (\cite {wa}) as well as for graphic $\lambda$-hypersurfaces (\cite{…

We prove that if $\omega _1$ and $\omega _2$ are moderate weights and $\mascB$ is a suitable (quasi-)Banach function space, then a necessary and sufficient condition for the embedding $i\, :\, M (\omega _1,\mascB )\to M (\omega _2,\mascB )$…

The moduli space of slope-stable vector bundles on a normal projective variety over an algebraically closed field of characteristic $p\geq 0$ is stratified with respect to the decomposition type. On a smooth projective curve of genus at…

Take an irreducible smooth complex projective curve $X$ of genus $g$, with $g\,\geq\, 3$. Let $r$ be an even positive integer. We prove that the Brauer group of the moduli stack of stable parabolic $\textnormal{PSp}(r,\mathbb{C})$--bundles…

The goal of the paper is to study the limiting behavior of the Weierstrass measures on a smooth curve of genus $g\geqslant 2$ as the curve approaches a certain nodal stable curve represented by a point in the Deligne-Mumford…

We study the moduli problem of pairs consisting of a rank 2 vector bundle and a nonzero section over a fixed smooth curve. The stability condition involves a parameter; as it varies, we show that the moduli space undergoes a sequence of…

Optimal transport is widely used to learn distributions, enforce distributional constraints, and model uncertainty. In applications, transport losses are often computed from samples through tractable representations, such as one-dimensional…

The geodesic problem in Wasserstein spaces with a metric perturbed by a conformal factor is considered, and necessary optimality conditions are estabilished in a case where this conformal factor favours the spreading of the probability…

In this article, we establish necessary and sufficient viability conditions for continuity inclusions over the 1-Wasserstein space. Depending on the regularity properties of the dynamics, we derive two results which are based on fairly…

Euler and Betti curves of stochastic processes defined on a $d$-dimensional compact Riemannian manifold which are almost surely in a Sobolev space $W^{n,s}(X,\mathbb{R})$ (with $d<n$) are stable under perturbations of the distributions of…

Let $q>1$, $(1-\frac{1}{q})a\geq 1$ and let $\Omega\subset \mathbb{R}^2$ be Lipschitz domain. We show that planar mappings in the second order Sobolev space $f\in W^{2,q}(\Omega,\mathbb{R}^2)$ with $|J_f|^{-a}\in L^1(\Omega)$ are…

This note gives a self-contained overview of some important properties of the Gromov-Wasserstein (GW) distance, compared with the standard linear optimal transport (OT) framework. More specifically, I explore the following questions: are GW…

The paper is devoted to studying the stability of random sampling in a localized reproducing kernel space. We show that if the sampling set on $\Omega$ (compact) discretizes the integral norm of simple functions up to a given error, then…

We generalise a result of Sawyer to show the following: For each y\in R^p and w\in R^q let \Gamma(y,w) be a measurable d-dimensional surface in R^n. Under conditions on the number of parameters and smoothness assumptions, there exists a set…

Let $\Omega$ be a convex open set in $\mathbb R^n$ and let $\Lambda_k$ be a finite subset of $\Omega$. We find necessary geometric conditions for $\Lambda_k$ to be interpolating for the space of multivariate polynomials of degree at most…

We give some necessary conditions and sufficient conditions for the compactness of the embedding of Sobolev spaces $W^{1,p}(\Omega,w) \to L^p(\Omega,w),$ where $w$ is some weight on a domain $\Omega \subset \Real^n$.

We prove necessary density conditions for sampling in spectral subspaces of a second order uniformly elliptic differential operator on $R^d$ with slowly oscillating symbol. For constant coefficient operators, these are precisely Landaus…