相关论文: Bohr--Favard Inequality for differences and consta…
We study a variation of the Shepard approximation scheme by introducing a dilation factor into the base function, which synchronizes with the Hausdorff distance between the data set and the domain. The novelty enables us to establish an…
The Brunn-Minkowski and Pr\'{e}kopa-Leindler inequalities admit a variety of proofs that are inspired by convexity. Nevertheless, the former holds for compact sets and the latter for integrable functions so it seems that convexity has no…
In this paper, two double Jordan-type inequalities are introduced that generalize some previously established inequalities. As a result, some new upper and lower bounds and approximations of the sinc function are obtained. This extension of…
We prove various extensions of the Loomis-Whitney inequality and its dual, where the subspaces on which the projections (or sections) are considered are either spanned by vectors $w_i$ of a not necessarily orthonormal basis of…
In this paper we prove that the complex polynomial Bohnenblust-Hille constant for $2$-homogeneous polynomials in ${\mathbb C}^2$ is exactly $\sqrt[4]{\frac{3}{2}}$. We also give the exact value of the real polynomial Bohnenblust-Hille…
The goal of this paper is to push forward the study of those properties of log-concave measures that help to estimate their Poincar{\'e} constant. First we revisit E. Milman's result [40] on the link between weak (Poincar{\'e} or…
Given a mean zero functional $F$ of a Poisson measure on a metric space, we apply the Malliavin-Stein method to establish sharpened second-order Poincar\'e inequalities for $F/\sqrt{\operatorname{Var} (F)}$ in terms of fourth moments of…
We prove a sharp stability result concerning how close homothetic sets attaining near-equality in the Brunn-Minkowski inequality are to being convex. In particular, resolving a conjecture of Figalli and Jerison, we show there are universal…
We prove that the fluctuations of mesocopic linear statistics for orthogonal polynomial ensembles are universal in the sense that two measures with asymptotic recurrence coefficients have the same asymptotic mesoscopic fluctuations (under…
We write expressions connected with numerical differentiation formulas of order $2$ in the form of Stieltjes integral, then we use Ohlin lemma and Levin-Stechkin theorem to study inequalities connected with these expressions. In particular,…
The primary objective of this paper is to establish several sharp versions of improved Bohr inequality, refined Bohr-type inequality, and refined Bohr-Rogosinski inequality for the class of $K$-quasiconformal sense-preserving harmonic…
There is a two-component log-gas system with Boltzmann factor which provides an interpolation between the eigenvalue PDF for $\beta = 1$ and $\beta = 4$ invariant random matrix ensembles. The solvability of this log-gas system relies on the…
We prove several results related to a Logvinenko-Sereda type theorem on dominating sets for generalized doubling Fock spaces. In particular, we give a precise polynomial dependence of the sampling constant on the relative density parameter…
We show the pointwise version of the Ste\v{c}kin theorem on approximation by de la Vall\'ee-Poussin means. The result on norm approximation is also derived.
This article presents a simplified formulation for the weak Galerkin finite element method for the Stokes equation without using the degrees of freedom associated with the unknowns in the interior of each element as formulated in the…
Let ~$\veps_1, ..., \veps_m$ be i.i.d. random variables with $$P(\veps_i=1)= P(\veps_i= -1)=1/2,$$ and $X_m = \sum_{i=1}^m \veps_i.$ Let $Y_m $ be a normal random variable with the same first two moments as that of $X_m.$ There is a…
We derive an inequality relating the finite-frequency linear response and fluctuations of an observable in a physical system. The relation holds for arbitrary observables and perturbations in general Markovian dynamics, including over- and…
The Jack polynomials with prescribed symmetry are obtained from the nonsymmetric polynomials via the operations of symmetrization, antisymmetrization and normalization. After dividing out the corresponding antisymmetric polynomial of…
In this paper we prove an inequality for individual and uniform Diophantine exponents in the case of simultaneous approximation. This inequality is better than Jarnik's for small values of the uniform exponent.
This paper provides a discrete Poincar\'e inequality in $n$ space dimensions on a simplex $K$ with explicit constants. This inequality bounds the norm of the piecewise derivative of functions with integral mean zero on $K$ and all integrals…