Related papers: Polynomial Pickands functions
We examine combinatorial counting functions with two parameters, $n$ and $q$. For fixed $q$, these functions are (quasi-)polynomial in $n$. As $q$ varies, the degree of this polynomial is itself polynomial in $q$, as are the leading…
We propose a new class of estimators for Pickands dependence function which is based on the concept of minimum distance estimation. An explicit integral representation of the function $A^*(t)$, which minimizes a weighted $L^2$-distance…
The Brenke type generating functions are the polynomial generating functions of the form $$\sum_{n=0}^{\infty}{P_n(x )\over n!}t^n=A(t)B(xt), $$ where $A$ and $B$ are two formal power series subject to the conditions…
We established exact in order estimates an approximation of the Sobolev classes $W^{\boldsymbol{r}}_{p,\boldsymbol{\alpha}}(\mathbb{T}^d)$ of periodic functions of many variables with a bounded dominating mixed derivative. The approximation…
This paper mainly studies problems about so called "permutation polynomials modulo $m$", polynomials with integer coefficients that can induce bijections over Z_m={0,...,m-1}. The necessary and sufficient conditions of permutation…
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…
In this article, the 2-iterated Sheffer polynomials are introduced by means of generating function and operational representation. Using the theory of Riordan arrays and relations between the Sheffer sequences and Riordan arrays, a…
Let x be a random vector coming from any k-wise independent distribution over {-1,1}^n. For an n-variate degree-2 polynomial p, we prove that E[sgn(p(x))] is determined up to an additive epsilon for k = poly(1/epsilon). This answers an open…
Given a bivariate weight function defined on the positive quadrant of $\mathbb{R}^2$, we study polynomials in two variables orthogonal with respect to varying measures obtained by special modifications of this weight function. In…
The main aim of this paper is to provide a unified approach to deriving identities for the Bernstein polynomials using a novel generating function. We derive various functional equations and differential equations using this generating…
Recent work has shown the surprising power of low-degree sandwiching polynomial approximators in the context of challenging learning settings such as learning with distribution shift, testable learning, and learning with contamination. A…
We prove the existence of complex polynomials $p(z)$ of degree $n$ and $q(z)$ of degree $m<n$ such that the harmonic polynomial $ p(z) + \overline{q(z)}$ has at least $\lceil n \sqrt{m} \rceil$ many zeros. This provides an array of new…
The ring of dual numbers over a ring $R$ is $R[\alpha] = R[x]/(x^2)$, where $\alpha$ denotes $x+(x^2)$. For any finite commutative ring $R$, we characterize null polynomials and permutation polynomials on $R[\alpha]$ in terms of the…
The paper deals with (multidimensional and one-dimensional) Bochner-Phillips functional calculus. Bounded perturbations of Bernstein functions of (one or several commuting) semigroup generators on Banach spaces are considered, conditions…
We analyze the accuracy of the discrete least-squares approximation of a function $u$ in multivariate polynomial spaces $\mathbb{P}_\Lambda:={\rm span} \{y\mapsto y^\nu \,: \, \nu\in \Lambda\}$ with $\Lambda\subset \mathbb{N}_0^d$ over the…
Orthogonal polynomials have very useful properties in the solution of mathematical problems, so recent years have seen a great deal in the field of approximation theory using orthogonal polynomials. In this paper, we characterize the…
Inspired by a recent work of Mesnager, we present several new infinite families of quadratic ternary bent, near-bent and 2-plateaued functions from some known quadratic ternary bent functions. Meanwhile, the distribution of the Walsh…
Let us denote ${\cal V}$, the finite dimensional vector spaces of functions of the form $\psi(x) = p_n(x) + f(x) p_m(x)$ where $p_n(x)$ and $p_m(x)$ are arbitrary polynomials of degree at most $n$ and $m$ in the variable $x$ while $f(x)$…
We present a construction of partial spread bent functions using subspaces generated by linear recurring sequences (LRS). We first show that the kernels of the linear mappings defined by two LRS have a trivial intersection if and only if…
We propose a new description of Endofunctors of Module Categories, based upon a combinatorial category comprising finite sets and so-called mazes. Polynomial and numerical functors both find a natural interpretation in this frame-work.…