Related papers: Holonomic modules associated with multivariate nor…

For a holomorphic function f on a complex manifold M we explain in this article that the distribution associated to |f | 2$\alpha$ (Log|f | 2) q f --N by taking the corresponding limit on the sets {|f | $\ge$ $\epsilon$} when $\epsilon$…

We introduce linear holonomy on Poisson manifolds. The linear holonomy of a Poisson structure generalizes the linearized holonomy on a regular symplectic foliation. However, for singular Poisson structures the linear holonomy is defined for…

The purpose of this paper is to initiate a new attack on Arveson's resistant conjecture, that all graded submodules of the $d$-shift Hilbert module $H^2$ are essentially normal. We introduce the stable division property for modules (and…

The Hilbert function of a module over a positively graded algebra is of quasi-polynomial type (Hilbert--Serre). We derive an upper bound for its grade, i.e. the index from which on its coefficients are constant. As an application, we give a…

Let $\{f_{\lambda; j}\}_{\lambda\in V; 1\le j\le k}$ be families of holomorphic functions in the open unit disk $\Di\subset\Co$ depending holomorphically on a parameter $\lambda\in V\subset \Co^n$. We establish a Rolle type theorem for the…

This article addresses an equidistribution problem concerning the zeros of systems of random holomorphic sections of positive line bundles on compact K\"{a}hler manifolds and random polynomials on $\mathbb{C}^{m}$ in the setting of the…

The theory of polynomial-like maps is of fundamental importance in holomorphic dynamics. We study dynamical properties of a larger class of maps. Our main result is that, under some natural conditions, a map of this class has a completely…

We study multivariate entire functions and polynomials with non-negative coefficients. A class of {\bf Strongly Log-Concave} entire functions, generalizing {\it Minkowski} volume polynomials, is introduced: an entire function $f$ in $m$…

Here the polynomial interpolation approach is used to introduce the main results on multivariate normal algebraic systems. Next we bring a construction which shows that any standard algebraic system, with finite set of solutions, can be…

We develop a diagrammatic categorification of the polynomial ring $Z[x]$. Our categorification satisfies a version of Bernstein-Gelfand-Gelfand reciprocity property with the indecomposable projective modules corresponding to $x^n$ and…

In this paper, we investigate the geometric properties of complex-valued pluriharmonic mappings defined over convex Reinhardt domains in $\mathbb{C}^n$. We first establish a multidimensional analogue of the Noshiro-Warschawski Theorem,…

P\'olya's Positivstellensatz and Handelman's Positivstellensatz are known to be concrete instances of the abstract Archimedean Representation Theorem for (commutative unital) rings. We generalise the Archimedean Representation Theorem to…

Illumination complexes are examples of 'flat polyhedral complexes' which arise if several copies of a convex polyhedron (convex body) Q are glued together along some of their common faces (closed convex subsets of their boundaries). A…

Let $\cl{M}$ be a Hilbert module of holomorphic functions over a natural function algebra $\mathcal{A}(\Omega)$, where $\Omega \subseteq \bb{C}^m$ is a bounded domain. Let $\cl{M}_0\subseteq \cl{M}$ be the submodule of functions vanishing…

In this paper we define a class of polynomial functors suited for constructing coalgebras representing processes in which uncertainty plays an important role. In these polynomial functors we include upper and lower probability measures,…

We define a version of Hochschild homology and cohomology suitable for a class of algebras admitting compatible actions of bialgebras, called module algebras. We show this (co)homology, called Hopf--Hochschild (co)homology, can also be…

In this paper, we prove some normality criteria concerning transitivity of normality from one family of meromorphic functions to another which improve and generalize some recent results. We also prove some value distribution results for…

We look for algebraic certificates of positivity for functions which are not necessarily polynomial functions. Similar questions were examined earlier by Lasserre and Putinar and by Putinar. We explain how these results can be understood as…

We study the growth of representations of the Lie algebra of vector fields on the affine space that admit a compatible action of the polynomial algebra. We establish the Bernstein inequality for these representations, enabling us to focus…

Orthogonal polynomials with respect to the hypergeometric distribution on lattices in polyhedral domains in ${\mathbb R}^d$, which include hexagons in ${\mathbb R}^2$ and truncated tetrahedrons in ${\mathbb R}^3$, are defined and studied.…