相关论文: Adventures in harmonic analysis

These informal notes briefly discuss some basic topics in harmonic analysis along the lines of convolutions and Fourier transforms.

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.

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

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

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

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…

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

These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.

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

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,…

Phase-space analysis or time-frequency analysis can be thought as Fourier analysis simultaneously both in time and in frequency, originating from signal processing and quantum mechanics. On groups having unitary Fourier transform, we…

These informal notes deal with some topics related to analysis on metric spaces.

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

An overview of some basic notions is given, especially with an eye towards somewhat "fractal" examples, such as infinite products of cyclic groups, p-adic numbers, and solenoids.

These notes, connected to a "potpourri" topics class currently underway, discuss some basic topics in analysis and connections with other areas of mathematics.

Here we look at some situations that are like the unit circle or the real line in some ways, but which can be more complicated or fractal in other ways.

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,…

We show that character analysis using Fourier series is possible, at least when a mathematical character is considered. Previous approaches to character analysis are somewhat not in the spirit of harmonic analysis.