Related papers: A density theorem for weighted Fekete sets
We prove an analogue of Kac's Theorem, describing the dimension vectors of indecomposable coherent sheaves, or parabolic bundles, over weighted projective lines. We use a theorem of Peng and Xiao to associate a Lie algebra to the category…
In this paper some links between the density of a set of integers and the density of its sumset, product set and set of subset sums are presented.
We obtain a fundamental inequality for a contraction with respect to a $C^*$-algebra valued metric space. As an application of this inequality a simple proof is given for the fixed point theorem in $C^*$-algebra valued metric space.
A unified version of Machado-Bishop theorem in weighted spaces is given. A number of applications illustrate its importance.
We prove strong convergence theorems of some iterative algorithms in a real uniformly smooth Banach space. The results presented extend, generalize and improve the corresponding results recently announced by many authors.
Let f_n denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let \Psi(t) be a positive continuous function such that \|\Psi f^{\beta}\|_{\infty}<\infty for some 0<\beta<1/2. Under natural…
Let $p$ be a prime. We study the distribution of points on a class of curves $C$ over $\mathbb{F}_p$ inside very small rectangles $B$ for which the Weil bound fails to give nontrivial information. In particular, we show that the…
We study the distribution of integral points on log varieties.
We first extend Calder\'on's transfer principle to weighted spaces, and then we apply our results to obtain some new weighted inequalities in ergodic theory and ergodic $H^1$ spaces.
We analyze the threshold network model in which a pair of vertices with random weights are connected by an edge when the summation of the weights exceeds a threshold. We prove some convergence theorems and central limit theorems on the…
We give a complete description of sampling and interpolation in the Bargmann-Fock space, based on a density concept of Beurling. Roughly speaking, a discrete set is a set of sampling if and only if its density in every part of the plane is…
In this paper, vector ultrametric spaces are introduced and a fixed point theorem is given for correspondences. Our main result generalizes a known theorem in ordinary ultrametric spaces.
The aim of this paper is to prove a fixed point theorem on a generalised cone metric spaces for maps satisfying general contractive type conditions.
In this article, we construct a $\theta$-density for the global sections of ample Hermitian line bundles on a projective arithmetic variety. We show that this density has similar behaviour to the usual density in the Arakelov geometric…
We introduce and study $\alpha$-embedded sets and apply them to generalize the Kuratowski Extension Theorem.
Kernel density estimation is a popular method for estimating unseen probability distributions. However, the convergence of these classical estimators to the true density slows down in high dimensions. Moreover, they do not define meaningful…
Hadwiger's theorem is a Helly-type theorem involving common transversals to families of convex sets instead of common intersections. Subsequently, Pollack and Wenger identified a necessary and sufficient condition, called a consistent…
We prove the density hypothesis for wide families of arithmetic orbifolds arising from all division quaternion algebras over all number fields of bounded degree. Our power-saving bounds on the multiplicities of non-tempered representations…
Variation of empirical Fr\'echet means on a metric space with curvature bounded above is encoded via random fields indexed by unit tangent vectors. A central limit theorem shows these random tangent fields converge to a Gaussian such field…
We prove a common extension of Bang's and Kadets' lemmas for contact pairs, in the spirit of the Colourful Carath\'eodory Theorem. We also formulate a generalized version of the affine plank problem and prove it under special assumptions.…