Related papers: A decomposition theorem on differential polynomial…

Necessary and sufficient conditions under which two real functions defined on the real interval can be separated by a polynomial are given. An immediate consequence of the main result is the existence of the polynomial separation of convex…

We prove a generalization of classical Montel's theorem for the mixed differences case, for polynomials and exponential polynomial functions, in commutative setting.

We prove thin-thick decompositions, for the class of Hardy martingales and thereby strengthen its square function characterization. We apply the underlying method to several classical martingale inequalities, for which we give new proofs .

We establish the basis of a discrete function theory starting with a Fischer decomposition for difference Dirac operators. Discrete versions of homogeneous polynomials, Euler and Gamma operators are obtained. As a consequence we obtain a…

In this paper, we consider linear differential equations satisfied by the generating function for Hermite polynomials and derive some new identities involving those polynomials.

We give a new and very concise proof of the existence of a holomorphic continuation for a large class of twisted multivariable zeta functions. To do this, we use a simple method of "decalage" that avoids using an integral representation of…

For any polynomial f with complex coefficients we find a remarkable subset of poles of the motivic zeta function. It is combinatorially determined by any log resolution and it admits an intrinsic interpretation in terms of contact loci of…

We give a decomposition formula for computing the state polytope of a reducible variety in terms of the state polytopes of its components.

We show that each member of a doubly infinite sequence of highly nonlinear expressions of Bernoulli polynomials, which can be seen as linear combinations of certain higher-order convolutions, is a multiple of a specific product of linear…

We study multivariate trigonometric polynomials, satisfying a set of constraints close to the known Strung-Fix conditions. Based on the polyphase representation of these polynomials relative to a general dilation matrix, we develop a simple…

We outline the construction of differential invariants for higher--rank tensors.

We develop a theory of arithmetic Newton polygons of higher order, that provides the factorization of a separable polynomial over a $p$-adic field, together with relevant arithmetic information about the fields generated by the irreducible…

We propose a method for constructing systems of polynomial equations that define submanifolds of degenerate binary forms of an arbitrary degeneracy degree. It is appropriate to call these systems of equations "higher discriminants".

We extend the well-known Shannon decomposition of Boolean functions to more general classes of functions. Such decompositions, which we call pivotal decompositions, express the fact that every unary section of a function only depends upon…

The purpose of this paper is to obtain some sufficient conditions to determine the relation between a meromorphic function and an L-function when certain differential polynomial generated by them sharing a one degree polynomial. The main…

We establish an edge of the wedge theorem for the sheaf of holomorphic functions with exponential growth at infinity and construct the sheaf of Laplace hyperfunctions in several variables. We also study the fundamental properties of the…

We provide simple criteria and algorithms for expressing homogeneous polynomials as sums of powers of independent linear forms, or equivalently, for decomposing symmetric tensors into sums of rank-1 symmetric tensors of linearly independent…

Let $s_0,s_1,s_2,\ldots$ be a sequence of rational numbers whose $m$th divided difference is integer-valued. We prove that $s_n$ is a polynomial function in $n$ if $s_n \ll \theta^n$ for some positive number $\theta$ satisfying $\theta <…

We prove an interpolation theorem for bounded free holomorphic functions.

The goal of this work is to characterize all second order difference operators of several variables that have discrete orthogonal polynomials as eigenfunctions. Under some mild assumptions, we give a complete solution of the problem.