Related papers: A density theorem for weighted Fekete sets

We obtain the convergence speed for Fekete points on uniformly polynomially cuspidal compact sets introduced by Pawlucki and Ple\'sniak. This is done by showing that these sets are $(\mathscr{C}^{\alpha}, \mathscr{C}^{\alpha'})$-regular in…

Let $K$ be a number field or a function field in one variable over a finite field, and let $K^{sep}$ be a separable closure of $K$. Let $C/K$ be a smooth, complete, connected curve. We prove a strong theorem of Fekete-Szego type for adelic…

A new proof following a suggestion of Kaplansky to use a result of Dixmier, and in this way avoid unbounded nets of operators, is given of the Kaplansky density theorem.

Let $S$ be a finite set of points in the plane and let $\mathcal{T}(S)$ be the set of intersection points between pairs of lines passing through any two points in $S$. We characterize all configurations of points $S$ such that iteration of…

We prove results about uniform convergence of densities in the free central limit theorem without assumptions of boundedness on the support.

We present variations on theorems of Mertens as special cases of Density Hypothesis. Moreover, we study a Serre's estimate concerning Lang-Weil estimate.

In this short note, we study the distribution of spreads in a point set $\mathcal{P} \subseteq \mathbb{F}_q^d$, which are analogous to angles in Euclidean space. More precisely, we prove that, for any $\varepsilon > 0$, if $|\mathcal{P}|…

We give an extension of the Fekete's Subadditive Lemma for a set of submultiplicative functionals on countable product of compact spaces. Our method can be considered as an unfolding of the ideas [1]Theorem 3.1 and our main result is an…

We characterize sampling and interpolating sets with derivatives in weighted Fock spaces on the complex plane in terms of their weighted Beurling densities.

In this paper, we classify the class of constant weighted curvature curves in the plane with a log-linear density, or in other words, classify all traveling curved fronts with a constant forcing term in $\Bbb R^2.$ The classification gives…

We show that if a non-trivial measure in the plane admits, at almost every point, positive and finite $\alpha$-dimensional density with respect to some norm, then $\alpha$ must be an integer.

Starting from first principles, we formulate a theory of wave packet propagation in a nonlinear, disordered medium of any dimension, through the derivation of a Fokker-Planck transport equation. Our theory is based on a diagrammatic…

We prove that smooth $C^\infty$ functions are dense in weighted fractional Sobolev spaces on an arbitrary open set, under some mild conditions on the weight. We also obtain a~similar result in non-weighted spaces defined by some kernel…

We prove that a nonempty, proper subset $S$ of the complex plane can be approximated in a strong sense by polynomial filled Julia sets if and only if $S$ is bounded and $\hat{\mathbb{C}} \setminus \textrm{int}(S)$ is connected. The proof…

We prove two-ends Furstenberg estimates in the plane for a Katz-Tao $(\delta,t)$-set of lines, for general $t\in[0,2]$.

In this paper we prove transference inequalities for regular and uniform Diophantine exponents in the weighted setting. Our results generalize the corresponding inequalities that exist in the `non-weighted' case.

In this paper, we establish some fixed point theorems in ordered partial metric spaces. An example is given to illustrate our obtained results.

It is showed that on a plane with a radial density the Four Vertex Theorem holds for the class of all simple closed curves if and only if the density is constant. But for the class of simple closed curves that are invariant under a rotation…

In a previous paper [Phys. Rev. A 105, 042205 (2022)], the distribution of resonance poles in the complex plane of the wavenumber $k$ associated to the multiple scattering of a quantum particle in a random point field was numerically…

We give an elementary proof of an analogue of Fej\'er's theorem in weighted Dirichlet spaces with superharmonic weights. This provides a simple way of seeing that polynomials are dense in such spaces.