Related papers: Bernstein- and Markov-type inequalities
The present paper is about Bernstein-type estimates for Jacobi polynomials and their applications to various branches in mathematics. This is an old topic but we want to add a new wrinkle by establishing some intriguing connections with…
It is known that for $C^{\infty}$ determining sets Markov's property is equivalent to Bernstein's property. The purpose of this paper is to prove an analogous result in the case of compact subsets of algebraic varieties.
Bernstein's classical inequality asserts that given a trigonometric polynomial $T$ of degree $n\geq1$, the sup-norm of the derivative of $T$ does not exceed $n$ times the sup-norm of $T$. We present various approaches to prove this…
We extend a general Bernstein-type maximal inequality of Kevei and Mason (2011) for sums of random variables.
The paper studies Bernstein type inequalities for restrictions of holomorphic polynomials to graphs $\Gamma_f\subset\mathbb C^{n+m}$ of holomorphic maps $f:\mathbb C^n\rightarrow\mathbb C^m$. We establish general properties of exponents in…
The present paper is devoted to the study of Jensen-Mercer-type inequalities. Our results generalize and improve some earlier results in the literature.
We introduce here a generalization of the modified Bernstein polynomials for Jacobi weights using the $q$-Bernstein basis proposed by G.M. Phillips to generalize classical Bernstein Polynomials. The function is evaluated at points which are…
It is be shown that the sequence of Bernstein polynomials for a function of several variables converges to this function uniformly along with every partial derivative of any order, provided that the latter derivative is well defined and…
Several families of sharp Bernstein inequalities are established on the weighted $L^2$ space over parabolic domains, which include bounded or unbounded rotational paraboloids and parabolic surfaces. The main tool is a second-order…
In this paper we generalize the known DDVV-type inequalities for real (skew-)symmetric and complex (skew-)Hermitian matrices to arbitrary real, complex and quaternionic matrices. Inspired by the Erd\H{o}s-Mordell inequality, we establish…
We continue our investigation of the intertwining relations for Markov semigroups and extend the results of [9] to multi-dimensional diffusions. In particular these formulae entail new functional inequalities of Brascamp-Lieb type for…
In this paper we give sharp $L_p$ Markov type inequalities for derivatives of multivariate polynomials for a wide family of UPC domains.
We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…
Let $S_N$ be the sum of vector-valued functions defined on a finite Markov chain. An analogue of the Bernstein--Hoeffding inequality is derived for the probability of large deviations of $S_N$ and relates the probability to the spectral gap…
We survey various classical results on invariants of polynomials, or equivalently, of binary forms, focussing on explicit calculations for invariants of polynomials of degrees 2, 3, 4.
This is an expository survey on the theory of Bernstein-Sato polynomials with special emphasis in its recent developments and its importance in commutative algebra.
We consider the $*$-Markov equation for the symmetric Laurent polynomials in three variables with integer coefficients, which is an equivariant analog of the classical Markov equation for integers. We study how the properties of the Markov…
In this article we present a Bernstein inequality for sums of random variables which are defined on a graphical network whose nodes grow at an exponential rate. The inequality can be used to derive concentration inequalities in…
We modify the classical Bernstein's inequality for the sums of independent centered random variables (r.v.) in the terms of relative tails or moments. We built also some examples in order to show the exactness of offered results.
Two types of Bernstein inequalities are established on the unit ball in $\mathbb{R}^d$, which are stronger than those known in the literature. The first type consists of inequalities in $L^p$ norm for a fully symmetric doubling weight on…