Related papers: On the convolution of convex 2-gons

We study homogenization by Gamma-convergence of periodic multiple integrals of the calculus of variations when the integrand can take infinite values outside of a convex set of matrices.

We study a class of corner growth models in which the weights are either all exponentially or all geometrically distributed. The parameter of the distribution at site $(i, j)$ is $a_i+b_j$ in the exponential case and $a_ib_j$ in the…

Extending classical results on polytopal approximation of convex bodies, we derive asymptotic formulas for the weighted approximation of smooth convex functions by piecewise affine convex functions as the number of their facets tends to…

This paper is devoted to the study of a convolution structure denoted by $*_{\alpha}$, which is defined via the Hartley--Bessel transform. This concept was introduced in a recent work by F. Bouzeffour [\emph{J. Pseudo-Differ. Oper. Appl.},…

The local (central) limit theorem precisely describes the behavior of iterated convolution powers of a probability distribution on the $d$-dimensional integer lattice, $\mathbb{Z}^d$. Under certain mild assumptions on the distribution, the…

Let $\Omega$ be a bounded closed convex set in ${\mathbb R}^d$ with non-empty interior, and let ${\cal C}_r(\Omega)$ be the class of convex functions on $\Omega$ with $L^r$-norm bounded by $1$. We obtain sharp estimates of the…

We study the topology of polynomial functions by deforming them generically. We explain how the non-conservation of the total ``quantity'' of singularity in the neighbourhood of infinity is related to the variation of topology in certain…

We study the boundary behaviour of a variant of the Fridman's invariant function (defined in terms of the Bergman metric) on Levi corank one domains, strongly pseudoconvex domains, smoothly bounded convex domains in $ \mathbb{C}^n $ and…

We give a proof of the Donnelly-Fefferman growth bound of Laplace-Beltrami eigenfunctions which is probably the easiest and the most elementary one. Our proof also gives new quantitative geometric estimates in terms of curvature bounds…

We find necessary and sufficient conditions on the convolution kernels $ \varphi $ so that certain operators on twisted Fock spaces $\mathcal{F}^\lambda(\C^{2n})$ are bounded.

In this article, we determine two point distortion theorem and sharp coefficient estimates for the families of close-to-convex harmonic mappings whose analytic part is a convex function of order $\alpha$. By making use of these results, we…

In this paper we deal with edge-to-edge, irreducible decompositions of a centrally symmetric convex $(2k)$-gon into centrally symmetric convex pieces. We prove an upper bound on the number of these decompositions for any value of $k$, and…

In this paper, a new lemma is proved and inequalities of Simpson type are established for co-ordinated convex functions and bounded functions.

We prove several variations on the results of Ricci and Travaglini concerning bounds for convolution with all rotations of a measure supported by a fixed convex curve in the plane. Estimates are obtained for averages over higher-dimensional…

An analytical approach to convolution of functions, which appear in perturbative calculations, is discussed. An extended list of integrals is presented.

A compactly supported distribution is called invertible in the sense of Ehrenpreis-H\"ormander if the convolution with it induces a surjection from $\mathcal{C}^{\infty}(\mathbb{R}^{n})$ to itself. We give sufficient conditions for radial…

We prove bounds for the covering numbers of classes of convex functions and convex sets in Euclidean space. Previous results require the underlying convex functions or sets to be uniformly bounded. We relax this assumption and replace it…

We show that for every connected analytic subvariety $V$ there is a pseudoconvex set $\Omega$ such that every bounded matrix-valued holomorphic function on $V$ extends isometrically to $\Omega$. We prove that if $V$ is two analytic disks…

The central purpose of the present paper is to study boundary behavior of squeezing functions on bounded domains. We prove that the squeezing function of a strongly pseudoconvex domain tends to 1 near the boundary. In fact, such an estimate…

Marx and Strohh\"acker showed around in 1933 that $f(z)/z$ is subordinate to $1/(1-z)$ for a normalized convex function $f$ on the unit disk $|z|<1.$ Brickman, Hallenbeck, MacGregor and Wilken proved in 1973 further that $f(z)/z$ is…