Related papers: Continuity properties of best analytic approximati…

We present an approximation theorem for continuous non-decreasing functions on compact preordered spaces, leading to an algebraic characterization of their corresponding function spaces. As an application, we prove that the family of…

A real valued function defined on a subset $E$ of $\mathbb{R}$, the set of real numbers, is $\rho$-statistically downward continuous if it preserves $\rho$-statistical downward quasi-Cauchy sequences of points in $E$, where a sequence…

In this work, the notions of normal cones at infinity to unbounded sets and limiting and singular subdifferentials at infinity for extended real value functions are introduced. Various calculus rules for these notions objects are…

We prove that the gradient of any bounded subharmonic function is upper semi-continuous, provided that its super-level sets can be touched from the exterior by uniform $C^{1,\text{Dini}}$ domains at every point. This idea extends to a class…

The aim of this paper is to characterize those linear maps from a von Neumann factor $\A$ into itself which preserve the extreme points of the unit ball of $\A$. For example, we show that if $\A$ is infinite, then every such linear…

We obtain an exact necessary and sufficient condition for the existence and uniqueness of equilibrium asset prices in infinite horizon, discrete-time, arbitrage free environments. Through several applications we show how the condition…

We prove a stability version of a general result that bounds the permanent of a matrix in terms of its operator norm. More specifically, suppose $A$ is an $n \times n$ matrix over $\mathbb{C}$ (resp. $\mathbb{R}$), and let $\mathcal{P}$…

The notion of supershift generalizes that one of superoscillation and expresses the fact that the sampling of a function in an interval allows to compute the values of the function outside the interval. In a previous paper we discussed the…

We establish a strong unique continuation property for the subelliptic Baouendi operator under the presence of zero-order perturbations satisfying an almost Hardy-type growth condition. In particular, the admissible class includes both…

This paper extends previous work from arxiv:1702.05223, which shows that the main theorem of Morse theory holds for a large class of functions on singular spaces, where the function and the underlying singular space are required to satisfy…

We introduce notions of absolutely continuous functionals and representations on the non-commutative disk algebra $A_n$. Absolutely continuous functionals are used to help identify the type L part of the free semigroup algebra associated to…

Sufficient and necessary conditions on the spectral measure of a self-adjoint operator $A$, acting in a Hilbert space, are obtained, under which for any continuous scalar function the operator function $\phi(A+\gamma B)$ is holomorphic with…

Let $X$ be a compact metric space, and let $A$ be a pure $\mathrm{C}^*$-algebra. We show that $C(X,A)$ is pure whenever $A$ is simple; or every quotient of $A$ is stably finite (e.g., $A$ has stable rank one). Using permanence properties of…

In this paper, we study the smoothness of the density function of absolutely continuous measures supported on random self-similar sets on the line. We show that the natural projection of a measure with symbolic local dimension greater than…

We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…

Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…

The primary purpose of this article is to show that a certain natural set of axioms yields a completeness result for continuous first-order logic. In particular, we show that in continuous first-order logic a set of formulae is (completely)…

We consider the problem of closeness of solutions of an exact and an averaged difference equations on an infinite interval. Appropriate assertions are derived from one special theorem on the stability under constantly acting perturbations.

The s-th forward difference sequence that tends to zero, inspired by the consecutive terms of a sequence approaching zero, is examined in this study. Functions that take sequences satisfying this condition to sequences satisfying the same…

Given a strictly positive measure, we characterize inner semicontinuous solid convex-valued mappings for which continuous functions which are selections almost everywhere are selections. This class contains continuous mappings as well as…