Related papers: Boundary relative extremal functions
We establish bounds on a finite separable extension of function fields in terms of the relative class number, thus reducing the problem of classifying extensions with a fixed relative class number to a finite computation. We also solve the…
In the general setting of a locally compact Abelian group $G$, the Delsarte extremal problem asks for the supremum of integrals over the collection of continuous positive definite functions $f: G \to \mathbb{R}$ satisfying $f(0) = 1$ and…
This article contains several results for \lambda-Robertson functions, i.e., analytic functions $f$ defined on the unit disk $D$ satisfying $f(0) = f'(0)-1=0$ and $Re e^{-i\lambda} {1+zf"(z)/f'(z)} > 0$ in $D$, where $\lambda \epsilon…
We prove fractional order Hardy inequalities on open sets under a combined fatness and visibility condition on the boundary. We demonstrate by counterexamples that fatness conditions alone are not sufficient for such Hardy inequalities to…
In recent years some near-optimal estimates have been established for certain sum-product type estimates. This paper gives some first extremal results which provide information about when these bounds may or may not be tight. The main tool…
In this paper we develop new extremal principles in variational analysis that deal with finite and infinite systems of convex and nonconvex sets. The results obtained, unified under the name of tangential extremal principles, combine primal…
In this paper we introduce new notions of local extremality for finite and infinite systems of closed sets and establish the corresponding extremal principles for them called here rated extremal principles. These developments are in the…
This paper studies and bounds the effects of approximating loss functions and credal sets on choice functions, under very weak assumptions. In particular, the credal set is assumed to be neither convex nor closed. The main result is that…
We investigate the theory of finite observables, i.e., resolutions of the finite-dimensional identity by means of positive operators, that have a physical interpretation in terms of measurement schemes. We focus on extremal and rank-one…
Although much research has been devoted to extremal problems on non-overlapping domains little is known about all solutions of this problems. We generalized some of this problems on the case of more general systems of points. It was solved…
The aim of this short note is to give an alternative proof, which applies to functions of bounded variation in arbitrary domains, of an inequality by Maz'ya that improves Friedrichs inequality. A remarkable feature of such a proof is that…
In this paper the concept of measure of noncompactness is applied to prove the existence of solution for a boundary value problem for an infinite system of second order differential equations in $\ell_{p}$ space. We change the boundary…
We propose a family of boundary terms for the action of a causal set with a spacelike boundary. We show that in the continuum limit one recovers the Gibbons-Hawking-York boundary term in the mean. We also calculate the continuum limit of…
Shape estimation and object reconstruction are common problems in image analysis. Mathematically, viewing objects in the image plane as random sets reduces the problem of shape estimation to inference about sets. Currently existing…
We establish upper and lower bounds with matching leading terms for tails of weighted sums of two-sided exponential random variables. This extends Janson's recent results for one-sided exponentials.
We study Edgeworth expansions in limit theorems for self-normalized sums. Non-uniform bounds for expansions in the central limit theorem are established while only imposing minimal moment conditions. Within this result, we address the case…
A central limit theorem for arrays of symmetric row-wise exchangeable random variables is presented. The result is valid for finite and infinite extendable and non-extendable sequences. Unlike most reported versions of the central limit…
A unifying framework for some extremal problems on locally compact Abelian groups is considered, special cases of which include the Delsarte and Tur\'an extremal problems. A slight variation of the extremal problem is introduced and the…
In the present paper we shall establish n-dimensional Hardy's inequalities with non-doubling weight functions of the distance to the boundary, where the boundary is a $C^2$ class bounded domain of $R^N$. This work is essentially based on…
This paper proves several weak limit theorems for the joint version of extreme order statistics and partial sums of independently and identically distributed random variables. The results are also extended to almost sure limit version.