Related papers: Sandwich Bernstein-Sato Polynomials and Bernstein'…
We solve a special type of linear systems with coefficients in multivariate polynomial rings. These systems arise in the computation of parametric Bernstein-Sato polynomials associated with certain hypergeometric ideals in the Weyl algebra.
We consider a sequence of composite Bernstein operators and the quadrature formulae associated with them. Upper bounds for the approximation error of continuous functions and for the approximation of integrals of continuous functions are…
Consider the diagonal action of the special orthogonal group on the direct sum of a finite number of copies of the standard representation--the underlying field is assumed to be algebraically closed and of characteristic not equal to two.…
In this note we determine the Bernstein-Sato polynomial $b_Q(s)$ of a generic central arrangement $Q=\prod_{i=1}^kH_i$ of hyperplanes. We establish a connection between the roots of $b_Q(s)$ and the degrees of the generators for the top…
For the p-adic group G=SL (2) , we present results of the computations of the sums of the Bernstein projectors of a given depth. Motivation for the computations is based on a conversation with Roger Howe in August 2013. The computations are…
This work obtains sharp closed-form exponential concentration inequalities of Bernstein type for the ubiquitous beta distribution, improving upon sub-gaussian and sub-gamma bounds previously studied in this context. The proof leverages a…
We summarize researches - in great deal jointly with my host Y. Sarantopoulos and his PhD. students V. Anagnostopoulos and A. Pappas - started by a Marie Curie fellowship in 2001 and is still continuing. The project was to study…
We prove a weak converse estimate for the simultaneous approximation by several forms of the Bernstein polynomials with integer coefficients. It is stated in terms of moduli of smoothness. In particular, it yields a big $O$-characterization…
For self-normalized martingales with conditionally symmetric differences, de la Pe\~{n}a [A general class of exponential inequalities for martingales and ratios. Ann. Probab. 27, No.1, 537-564] established the Gaussian type exponential…
A generalization of the Bernstein matrix concentration inequality to random tensors of general order is proposed. This generalization is based on the use of Einstein products between tensors, from which a strong link can be established…
This note is devoted to several results about frequency localized functions and associated Bernstein inequalities for higher order operators. In particular, we construct some counterexamples for the frequency-localized Bernstein…
We show somewhat unexpectedly that whenever a general Bernstein-type maximal inequality holds for partial sums of a sequence of random variables, a maximal form of the inequality is also valid.
We show that if $f\in \mathcal{O}_X(X)$ and $g\in \mathcal{O}_Y(Y)$ are nonzero regular functions on smooth complex algebraic varieties $X$ and $Y$, then the Bernstein-Sato polynomial of the product function $fg \in \mathcal{O}_{X\times…
We make quantitative improvements to recently obtained results on the structure of the image of a large difference set under certain quadratic forms and other homogeneous polynomials. Previous proofs used deep results of Benoist-Quint on…
Large deviation inequalities for ergodic sums is an important subject since the seminal contribution of Bernstein for independent random variables with finite variances, followed by the Chernoff method and the Hoefding result for…
We give an elementary introduction to some recent polyhedral techniques for understanding and solving systems of multivariate polynomial equations. We provide numerous concrete examples and illustrations, and assume no background in…
It is demonstrated that multiplier methods naturally yield better constants in strong converse inequalities for the Bernstein-Durrmeyer operator. The absolute constants obtained in some of the inequalities are independent of the weight and…
A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under recent consideration is to enforce bounds constraints on the approximating polynomial. In…
Incomplete U-statistics have been proposed to accelerate computation. They use only a subset of the subsamples required for kernel evaluations by complete U-statistics. This paper gives a finite sample bound in the style of Bernstein's…
In this paper we show that the weighted Bernstein-Walsh inequality in logarithmic potential theory is sharp up to some new universal constant, provided that the external field is given by a logarithmic potential. Our main tool for such…