相关论文: A beginner's guide to analysis on metric spaces

The setting of metric spaces is very natural for numerous questions concerning manifolds, norms, and fractal sets, and a few of the main ingredients are surveyed here.

We collect some classical results related to analysis on the Riemann surfaces. The notes may serve as an introduction to the field: we suppose that the reader is familiar only with the basic facts from topology and complex analysis. the…

This paper presents a distance function between sets based on an average of distances between their elements. The distance function is a metric if the sets are non-empty finite subsets of a metric space. It can be applied to produce various…

This paper is a survey about the Thurston metric on the Teichm\"uller space. The central issue is the constructions of extremal Lipschitz maps between hyperbolic surfaces. We review several constructions, including the original work of…

This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…

This is a brief introduction to the basic concepts of topology. It includes the basic constructions, discusses separation properties, metric and pseudometric spaces, and gives some applications arising from the use of topology in computing.

These informal notes deal with Fourier series in one or more variables, Fourier transforms in one variable, and related matters.

These informal notes consider Fourier transforms on a simple class of nice functions and some basic properties of the Fourier transform.

We introduce Hausdorff operators over the unit disc and give conditions for boundedness of such operator in Bloch, Bergman, and Hardy spaces on the disc. Identity approximation by Hausdorff operators is also considered.

This brief note, written for non-specialists, aims at drawing an introductive overview of the multiverse issue.

In this paper we introduce the notions of statistical convergence and statistical Cauchyness of sequences in a metric-like space. We study some basic properties of these notions

This paper addresses problems in functional metric geometry that arise in the study of data such as signals recorded on geometric domains or on the nodes of weighted networks. Datasets comprising such objects arise in many domains of…

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,…

We study metric spaces homeomorphic to a closed oriented manifold from both geometric and analytic perspectives. We show that such spaces (which are sometimes called metric manifolds) admit a non-trivial integral current without boundary,…

The Lipschitz geometry of segments of the infinite Hamming cube is studied. Tight estimates on the distortion necessary to embed the segments into spaces of continuous functions on countable compact metric spaces are given. As an…

Additional integral inequalities are obtained for integrals of the differences of subharmonic functions by Borel measures on balls in a multidimensional Euclidean space. These integrals are still estimated from above through the Nevanlinna…

These informal notes deal with a number of questions related to sums and integrals in analysis.

General expository paper concerning topics in Hilbert spaces, spectral theory, and harmonic analysis. The preliminary section includes basic Banach algebra and Hilbert space theory with a digression on Riesz bases. The second and third…

Recently, Le Donne and the author introduce a notion of intrinsically Lipschitz graphs in metric spaces. The idea of this paper is to investigate about the properties of the intrinsically Lipschitz constants. More precisely, we give the…

This article aims to explore the most recent developments in the study of the Hilbert matrix, acting as an operator on spaces of analytic functions and sequence spaces. We present the latest advances in this area, aiming to provide a…