Related papers: Structural aspects of extremal functions in the Kr…
The Krzy\.z conjecture concerns the largest values of the Taylor coefficients of a non-vanishing analytic function bounded by one in modulus in the unit disk. It has been open since 1968 even though information on the structure of extremal…
We discuss the problem where the extremal function in embedding theorem of some (generally speaking, non-integer) order is the constant function. We obtain the necessary and sufficient conditions of this.
An extremal point of a positive threshold Boolean function $f$ is either a maximal zero or a minimal one. It is known that if $f$ depends on all its variables, then the set of its extremal points completely specifies $f$ within the universe…
We use the formalism of the R{\'e}nyi entropies to establish the symmetry range of extremal functions in a family of subcriti-cal Caffarelli-Kohn-Nirenberg inequalities. By extremal functions we mean functions which realize the equality…
Our object of study is extremal functions which are defined by distance functions of convex bodies. These functions take values in the moduli spaces of algebraic and geometric objects associated with these ${\mathbb Z}$-modules (geometric…
This paper focus on the symmetry and symmetry breaking about the second order Hydrogen Uncertainty Principle. \emph{Firstly}, by choosing a suitable test function, we give a negative answer to the conjecture presented by Cazacu, Flynn and…
A geometric setup for constrained variational calculus is presented. The analysis deals with the study of the extremals of an action functional defined on piecewise differentiable curves, subject to differentiable, non-holonomic…
We show that if the minimum entropy for a polynomial with roots on the unit circle is attained by polynomials with equally spaced roots, then, under a generic hypothesis about the nature of the extremum, the Krzyz conjecture on the maximum…
Extremal functions are exhibited in Poincar\'e trace inequalities for functions of bounded variation in the unit ball ${\mathbb B}^n$ of the $n$-dimensional Euclidean space ${\mathbb R}^n$. Trial functions are subject to either a vanishing…
We prove the extremal function for $K_9^=$ minors, where $K_9^=$ denotes the complete graph $K_9$ with two edges removed. In particular, we show that any graph with $n$ vertices and at least $6n - 20$ edges either contains a $K_9^=$ minor…
The main result of this paper is some "annulus" formula for the relative extremal function in the context of Stein spaces (Theorem 1.1). Our result may be useful in the theory of the extension of separately holomorphic functions on…
The aim of this paper is to investigate the cone of non-negative, radial, positive-definite functions in the set of continuous functions on $\R^d$. Elements of this cone admit a Choquet integral representation in terms of the extremals. The…
In this paper, we study the extremal problem for the Strichartz inequality for the Schr\"{o}dinger equation on the $\mathbb{R} \times \mathbb{R}^2$; we provide a new proof to the characterization of the extremal functions. The only extremal…
Typically, in the dynamical theory of extremal events, the function that gauges the intensity of a phenomenon is assumed to be convex and maximal, or singular, at a single, or at most a finite collection of points in phase--space. In this…
The systematic study of Tur\'an-type extremal problems for edge-ordered graphs was initiated by Gerbner et al. arXiv:2001.00849. They conjectured that the extremal functions of edge-ordered forests of order chromatic number 2 are…
We prove three sharp estimates for the generalized Zalcman coefficient functional: one for the Hurwitz class, another for the Noshiro-Warschawski class, and yet another for the functions in the closed convex hull of convex univalent…
We make a study of Weinstein functionals, first defined in ~\cite{W}, on the hyperbolic space $\mathbb{H}^n$. We are primarily interested in the existence of Weinstein functional maximisers, or, in other words, existence of extremal…
We focus on two dependency quantities of a max-stable random field $X$ on some space $T$: the extremal coefficient function $\theta$ which we define on finite sets of $T$ and the extremal correlation function $\chi(s,t)=\lim_{x \uparrow…
In this paper, we investigate the extremal structure of the unit ball in the most general classes of Orlicz--Lorentz spaces. the characterizations of extreme points, strongly extreme points, and exposed points are given for Orlicz--Lorentz…
This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These…