Related papers: Directional Chebyshev Constants on the Boundary

In this paper, we obtain uniform bounds for a number of expressions that involve derivatives and integrals of modified Bessel functions. These uniform bounds are motivated by the need to bound such expressions in the study of variance-gamma…

We give a positive answer to a question of J. Doyle and J. Silverman about fields of definition of dynamical systems on $\mathbb{P}^{n}$. We prove that, for fixed $n$, there exists a constant $C_{n}$ such that every dynamical system…

Lower and upper bounds are explored for the uniform (Kolmogorov) and $L^2$-distances between the distributions of weighted sums of dependent summands and the normal law. The results are illustrated for several classes of random variables…

We investigate the size of fixed point sets of automorphisms of bounded domains in $\mathbb{C}^n$. In one complex variable, a nontrivial automorphism has at most two fixed points, but in higher dimensions fixed point sets need not be…

It has been proved by the authors that the (extended) Sadowsky functional can be deduced as the Gamma-limit of the Kirchhoff energy on a rectangular strip of height $\varepsilon$, as $\varepsilon$ tends to 0. In this paper we show that this…

We extend several Cheeger-type isoperimetric bounds for convex sets in Euclidean space, due to Bobkov and Kannan-Lov\'asz-Simonovits, to Riemannian manifolds having non-negative Ricci curvature. In order to extend Bobkov's bound, we require…

In the present note we prove a conjecture of Demailly for finite sets of sufficiently many very general points in projective spaces. This gives a lower bound on Waldschmidt constants of such sets. Waldschmidt constants are asymptotic…

We obtain a uniform linear bound for the Chevalley function at a point in the source of an analytic mapping that is regular in the sense of Gabrielov. There is a version of Chevalley's lemma also along a fibre, or at a point of the image of…

Extended Chebyshev spaces that also comprise the constants represent large families of functions that can be used in real-life modeling or engineering applications that also involve important (e.g. transcendental) integral or rational…

For "Riesz-like" kernels $K(x,y)=f(|x-y|)$ on $A\times A$, where $A$ is a compact $d$-regular set $A\subset \mathbb{R}^p$, we prove a minimum principle for potentials $U_K^\mu=\int K(x,y)d\mu(x)$, where $\mu$ is a Borel measure supported on…

We establish existence, uniqueness, and arbitrary order Sobolev regularity results for the second order parabolic equations with measurable coefficients defined on the conic domains $D$ of the type $$ D(M):=\left\{x\in R^d…

It is established a continuous boundary extension of some class of mappings. Under some additional conditions, we have established that this extension is light in the closure of the definition domain. Under some stronger conditions, we also…

On a compact three-dimensional Riemannian manifold with boundary, we prove the compactness of the full set of conformal metrics with positive constant scalar curvature and constant mean curvature on the boundary. This involves a blow-up…

Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.

In this paper, we study a part of approximation theory that presents the conditions under which a closed set in a normed linear space is proximinal or Chebyshev.

We show that weighted Bergman projections corresponding to radially symmetric weights on the unit disc are bounded on Sobolev spaces.

We give a simple proof of a Chernoff bound for the spectrum of a $k$-local Hamiltonian based on Weyl's inequalities. The complexity of estimating the spectrum's $\epsilon(n)$-th quantile up to constant relative error thus exhibits the…

This paper investigates the behavior of sets and functions at infinity by introducing new concepts, namely directional normal cones at infinity for unbounded sets, along with limiting and singular subdifferentials at infinity in the…

We survey results on Chebyshev polynomials centered around the work of H. Widom. In particular, we discuss asymptotics of the polynomials and their norms and general upper and lower bounds for the norms. Several open problems are also…

In this paper various notions of convexity of real functions with respect to Chebyshev systems defined over arbitrary subsets of the real line are introduced. As an auxiliary notion, a concept of a relevant divided difference and also a…