Related papers: Geometry of homogeneous polynomials in ${\mathbb R…
In the paper a Riemannian structure on the tangent bundle is defined by using a statistical structure $(g,\nabla)$ on the base manifold. Expressions for various curvatures of the structure are derived. Some rigidity results of the structure…
We consider degree-d forms on the Euclidean unit sphere. We specialize to our setting a genericity result by Nie obtained in a more general framework. We exhibit an homogeneous polynomial Res in the coefficients of f , such that if Res(f) =…
We obtain new uniqueness theorems for harmonic functions defined on the unit disc or in the half plane. These results are applied to obtain new resolvent descriptions of spectral subspaces of polynomially bounded groups of operators on…
The purpose of this note is to present several aspects of concentration phenomena in high dimensional geometry. At the heart of the study is a geometric analysis point of view coming from the theory of high dimensional convex bodies. The…
A polygonal surface in the pseudo-hyperbolic space H^(2,n) is a complete maximal surface bounded by a lightlike polygon in the Einstein universe Ein^(1,n) with finitely many vertices. In this article, we give several characterizations of…
This article is divided in two parts. In the first part we review some recent results concerning the expected number of real roots of random system of polynomial equations. In the second part we deal with a different problem, namely, the…
We provide two examples of complex homogeneous quadratic polynomials P on Banach spaces of the form l_1(I). The first polynomial P has both separable and nonseparable maximal zero subspaces. The second polynomial P has the property that…
The presented paper is devoted to statistical modeling of Gaussian scalar real random fields inside a three-dimensional sphere (ball). We propose a statistical model describing the spatial heterogeneity in a unit ball and a numerical…
We investigate projection constants within classes of multivariate polynomials over finite-dimensional real Hilbert spaces. Specifically, we consider the projection constant for spaces of spherical harmonics and spaces of homogeneous…
We prove some new results about the spacing between neighboring zeros of paraorthogonal polynomials on the unit circle. Our methods also provide new proofs of some existing results. The main tool we will use is a formula for the phase of…
Our first aim of this article is to establish several new versions of refined Bohr inequalities for bounded analytic functions in the unit disk involving Schwarz functions. Secondly, %as applications of these results, we obtain several new…
We begin by describing the unit ball of the free $p$-convex Banach lattice over a Banach space $E$ (denoted by ${\mathrm{FBL}}^{(p)}[E]$) as a closed solid convex hull of an appropriate set. Based on it, we show that, if a Banach space $E$…
We investigate the extremal properties of the unit ball of $L(X)_w^*$, the dual space of bounded linear operators defined on a Banach space $X$ equipped with the numerical radius norm. As an application of the present study, we obtain a…
In this paper, we first establish refined versions of the Bohr inequalities for the class of holomorphic functions from the unit ball $B_X$ of a complex Banach space $X$ into $\mathbb{C}$. As applications, we will establish refined Bohr…
In analogy with the classical Minkowski problem, necessary and sufficient conditions are given to assure that a given measure on the unit sphere is the cone-volume measure of the unit ball of a finite dimensional Banach space.
In this survey we present the most recent developments in the uniformization of metric surfaces, i.e., metric spaces homeomorphic to two-dimensional topological manifolds. We start from the classical conformal uniformization theorem of…
In this paper we introduce the concept of polynomial diagrams and its area for special polynomials.We study the properties of polynomial area diagrams. The formula for the area of an arbitrary polynomial diagram.
In this paper, using generalized metric projection, we propose a new extragradient method for finding a common element of the solutions set of a generalized equilibrium problem and a variational inequality for an $\alpha$-inverse-strongly…
For any natural $d \ge k \ge 2$ we calculate the cohomology groups of the space of homogeneous polynomials $R^2 \to R$ of degree $d$, which do not vanish with multiplicity $\ge k$ on real lines. For $k=2$ this problem provides the simplest…
Spaces of homogeneous polynomials on a Banach space are frequently equipped with quasinorms instead of norms. In this paper we develop a technique to replace the original quasi-norm by a norm in a dual preserving way, in the sense that the…