Related papers: Polynomial Pickands functions

In this paper a general theory of semi-classical matrix orthogonal polynomials is developed. We define the semi-classical linear functionals by means of a distributional equation $D(u A) = u B,$ where $A$ and $B$ are matrix polynomials.…

This paper is a survey of plurisubharmonic theory where the usual polynomial ring is replaced by a polynomial ring $\mathcal P^S(\mathbb C^n)$ where the $m$-th degree polynomials have exponents restricted to $mS$, where $S\subseteq \mathbb…

Two classes of ternary bent functions of degree four with two and three terms in the univariate representation that belong to the completed Maiorana-McFarland class are found. Binomials are mappings $\F_{3^{4k}}\mapsto\fthree$ given by…

We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms…

Let $\mathbb C$ be the set of complex numbers, and let $\mathcal P$ be a collection of complex polynomial maps in several variables. Assuming at least one $P\in\mathcal P$ depends on at least two variables, we classify all possibilities for…

We study polynomial functors in the incompressible category $\text{Ver}_4^+$, which can be viewed as super polynomial functors in characteristic 2. Concretely, we classify additive, exact and simple polynomial functors, and describe how…

In this work the interplay between matrix biorthogonal polynomials with respect to a matrix of linear functionals, the $k$-th associated matrix polynomials and the second kind matrix functions, is studied in terms of quasideterminants. A…

We give derivations of some basic results for the Bernstein approximation in $n$ variables that are useful in investigating copulas. It is shown that Bernstein approximations of copulas are again copulas. We exhibit a stochastic…

We consider multilinear Littlewood polynomials, polynomials in $n$ variables in which a specified set of monomials $U$ have $\pm 1$ coefficients, and all other coefficients are $0$. We provide upper and lower bounds (which are close for $U$…

In this article, a formulation of a point-collocation method in which the unknown function is approximated using global expansion in tensor product Bernstein polynomial basis is presented. Bernstein polynomials used in this study are…

We compare the yields of two methods to obtain Bernstein type pointwise estimates for the derivative of a multivariate polynomial in points of some domain, where the polynomial is assumed to have sup norm at most 1. One method, due to…

We consider the problem of computing matrix polynomials $p(X)$, where $X$ is a large dense matrix, with as few matrix-matrix multiplications as possible. More precisely, let $\Pi_{2^{m}}^*$ represent the set of polynomials computable with…

Motivated by numerical methods for solving parametric partial differential equations, this paper studies the approximation of multivariate analytic functions by algebraic polynomials. We introduce various anisotropic model classes based on…

Dual Bernstein polynomials of one or two variables have proved to be very useful in obtaining B\'{e}zier form of the $L^2$-solution of the problem of best polynomial approximation of B\'{e}zier curve or surface. In this connection, the…

We construct a set $M_d$ whose points parametrize families of Meixner polynomials in $d$ variables. There is a natural bispectral involution $b$ on $M_d$ which corresponds to a symmetry between the variables and the degree indices of the…

In this paper, we investigate the problem of finding tight linear lower bounding functions for multivariate polynomials over boxes. These functions are obtained by the expansion of polynomials into Bernstein form and using the linear least…

We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and have optimal dependence on the meshwidth and frequency when…

Inference over tails is performed by applying only the results of extreme value theory. Whilst such theory is well defined and flexible enough in the univariate case, multivariate inferential methods often require the imposition of…

Generalizations of some known results on the best, best linear and best one-sided approxima- tions by trigonometric polynomials of the classes of 2\pi - periodic functions presented in the form of convolutions to the case of set-valued…

We prove two identities for multivariate Bernstein polynomials on simplex, which are considered on a pointwise. In this paper, we study good approximations of Bernstein polynomials for every continuous functions on simplex and the higher…