相关论文: Elements of harmonic analysis

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

These informal notes concern some basic themes of harmonic analysis related to representations of groups.

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

These notes briefly discuss Fourier transforms of finite measures and extensions of Fourier integrals to points in complex domains.

Fourier Transforms is a first in a series of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such…

This is a brief survey which reviews some traditional themes in harmonic analysis and some more recent areas of activity, connected to "analysis on fractals" in particular.

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

Fourier Series is the second of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such as partial…

These informal notes briefly discuss Fourier inversion in terms of Gauss--Weierstrass kernels and summability.

The purpose of this article is to survey certain aspects of multilinear harmonic analysis related to notions of transversality. Particular emphasis will be placed on the multilinear restriction theory for the euclidean Fourier transform,…

These informal notes are concerned with sums and averages in various situations in analysis.

These notes briefly consider convolutions of tempered distributions with functions in the Schwartz class.

These notes are concerned with Abel sums and connections with analytic extensions of Fourier integrals.

These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.

In this brief survey we give an introduction to some aspects of "atoms" on metric spaces and their connection with linear operators.

These notes deal with a few properties of convolutions in the role of approximations to the identity.

These notes present a first graduate course in harmonic analysis. The first part emphasizes Fourier series, since so many aspects of harmonic analysis arise already in that classical context. The Hilbert transform is treated on the circle,…

In this short note we recall the definition of intrinsically harmonic forms, some known results and some open problems.

A number of topics in analysis are discussed, with emphasis on basic principles. There is some overlap with "Elements of linear and real analysis" (arXiv:math/0108030), with numerous changes in content and presentation since then.

These informal notes briefly discuss some basic topics involving Lipschitz functions, connectedness, and Hausdorff content in particular.