Related papers: A Bombieri-type inequality and equidistribution of…
In this paper we explore the connections between minimizers of the discrete logarithmic energy on the 2-dimensional sphere, univariate polynomials with optimal condition number in the Shub-Smale sense and a quotient involving norms of…
In his work on singularities, expanders and topology of maps, Gromov showed, using isoperimetric inequalities in graded algebras, that every real valued map on the $n$-torus admits a fibre whose homological size is bounded below by some…
We consider inequalities of Bombieri type for polynomials that need not be homogeneous, using the apolar inner product.
By discrete trigonometric norming inequalities on subintervals of the period, we construct norming meshes with optimal cardinality growth for algebraic polynomials on sections of sphere, ball and torus.
Companion results to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.
New results related to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.
In this paper we show a new inequality which generalizes to the unit sphere the Lebedev-Milin inequality of the exponentiation of functions on the unit circle. It may also be regarded as the counterpart on the sphere of the second…
Some related results to Pecaric's inequality in inner product spaces that generalises Bombieri's inequality, are given.
The aim of this paper is to state and prove polynomial analogues of the classical Manning inequality relating the topological entropy of a geodesic flow with the growth rate of the volume of balls in the universal covering. To this aim we…
The main aim of this article is to establish a sharp improvement of the classical Bohr inequality for bounded holomorphic mappings in the polydisk $\mathbb{P}\Delta(0;1_n)$. We also prove two other sharp versions of the Bohr inequality in…
We study inequalities connecting a product of uniform norms of polynomials with the norm of their product. Generalizing Gel'fond-Mahler inequality for the unit disk and Kneser-Borwein inequality for the segment $[-1,1]$, we prove an…
We will study algebraic hyper-surfaces on the real unit sphere $\mathcal S^{n-1}$ given by an homogeneous polynomial of degree d in n variables with the view point, rarely exploited, of Euclidian geometry using Bombieri's scalar product and…
A classical result of Erdos and Turan states that if a monic polynomial has small size on the unit circle and its constant coefficient is not too small, then its zeros cluster near the unit circle and become equidistributed in angle. Using…
The main aim of this article is to establish a sharp improvement of the classical Bohr inequality for bounded holomorphic mappings in the polydisk $\mathbb{D}^n$.We also prove two other sharp versions of the Bohr inequality in the setting…
We take a unifying and new approach toward polynomial and trigonometric approximation in an arbitrary number of variables, resulting in a precise and general ready-to-use tool that anyone can easily apply in new situations of interest. The…
We study a generalized Abreu Equation in $n$-dimensional polytopes and prove some differential inequalities for homogeneous toric bundles.
We obtain new sharp isoperimetric inequalities on a Riemannian manifold equipped with a probability measure, whose generalized Ricci curvature is bounded from below (possibly negatively), and generalized dimension and diameter of the convex…
We show that the size of codes in projective space controls structural results for zeros of odd maps from spheres to Euclidean space. In fact, this relation is given through the topology of the space of probability measures on the sphere…
In this paper, monic polynomials orthogonal with deformation of the Freud-type weight function are considered. These polynomials fullfill linear differential equation with some polynomial coefficients in their holonomic form. The aim of…
We generalize the Beckner's type Poincar\'e inequality \cite{Beckner} to a large class of probability measures on an abstract Wiener space of the form $\mu\star\nu$, where $\mu$ is the reference Gaussian measure and $\nu$ is a probability…