Related papers: Approximation of continuous functions on Fr\'echet…

We derive necessary and sufficient conditions for a continuous bounded function $f: R\to C$ to be a characteristic function of a probability measure. The Cauchy transform $K_f$ of $f$ is used as analytic continuation of $f$ to the upper and…

We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using…

The goal of this work is to study the space of continuous functions whose ergodic averages converge everywhere towards a continuous function. We will connect, as in the case of a metric study, the convergence of the ergodic averages and the…

In this paper, we consider certain topological properties along with certain types of mappings on these spaces defined by the notion of ideal convergence. In order to do that, we primarily follow in the footsteps of the earlier studies of…

The persistence diagram is an increasingly useful tool from Topological Data Analysis, but its use alongside typical machine learning techniques requires mathematical finesse. The most success to date has come from methods that map…

On any metric space, I provide an intrinsic characterization of those complex-valued functions which are uniform limits of Lipschitz functions. There are applications to function theory on complete Riemannian manifolds and, in particular,…

This paper develops a functional-analytic framework for approximating the push-forward induced by an analytic map from finitely many samples. Instead of working directly with the map, we study the push-forward on the space of locally…

Let $T$ be a topological space admitting a compatible proper metric, that is, a locally compact, separable and metrisable space. Let $\mathcal{M}^T$ be the non-empty set of all proper metrics $d$ on $T$ compatible with its topology, and…

When dealing with concrete problems in a function space on R^n, it is sometimes helpful to have a dense subspace consisting of functions of a particular type, adapted to the problem under consideration. We give a theorem that allows one to…

In this paper we study a sufficient conditions for continuous and almost continuous extensions of f to space X for an image space Y with different separation axioms.

Let X be a separable metric space and let \beta be the strict topology on the space of bounded continuous functions on X, which has the space of \tau-additive Borel measures as a continuous dual space. We prove a Banach-Dieudonne\'{e} type…

Generic approximation of entire functions by their Pad\'{e} approximants has been achieved in the past (\cite{3}). In the present article we obtain generic approximation of holomorphic functions on arbitrary open sets by sequences of their…

We consider the space of functions almost in $L_p$ and endow it with the topology of asymptotic $L_p$-convergence. This yields a completely metrizable topological vector space which, on finite measure spaces, coincides with the space of…

Let $E$ be an arbitrary subset of a Banach space $X$, $f: E \rightarrow \mathbb{R}$ be a function, and $G:E \rightrightarrows X^*$ be a set-valued mapping. We give necessary and sufficient conditions on $f, G$ for the existence of a…

We establish that a generalized H\"{o}lder continuous function on an $(m-2)$-Ahlfors regular compact set in $\mathbb{R}^m$ can be approximated by solutions of an elliptic equation, with the rate of approximation determined by the continuity…

Given a finite number of samples of a continuous set-valued function F, mapping an interval to non-empty compact subsets of $\mathbb{R}^d$, $F: [a,b] \to K(\mathbb{R}^d)$, we discuss the problem of computing good approximations of F. We…

We study approximation properties of the Fr\'{e}chet space of all continuously differentiable functions $\tau$ such that $\tau'(x)=o(1)$ and such that their Laplace transforms admit entire extensions to $\mathbb{C}$. As an application,…

It is well known that in $R^n$ , G{\^a}teaux (hence Fr{\'e}chet) differ-entiability of a convex continuous function at some point is equivalent to the existence of the partial derivatives at this point. We prove that this result extends…

We show that a fairly arbitrary Frechet space topology on the space of holomorphic functions on a domain controls the topology of uniform convergence on compact sets. In fact it turns out that the result we present can be proved more simply…

We study properties of continuous semi-homogeneous operators of degree $k$ via various functions (e.g. measures of noncompactness) on all bounded subsets of a Banach space. We prove necessary and sufficient conditions for these functions to…