相关论文: Some topics in complex and harmonic analysis

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

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

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 study the Fourier transforms of indicator functions of some special high-dimensional finite type domains and obtain estimates of the associated lattice point discrepancy.

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.

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…

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

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.

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

This paper surveys some selected topics in the theory of conformal metrics and their connections to complex analysis, partial differential equations and conformal differential geometry.

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 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,…

We develop a harmonic analysis on objects of some category $C_2$ of infinite-dimensional filtered vector spaces over a finite field. It includes two-dimensional local fields and adelic spaces of algebraic surfaces defined over a finite…

This paper discusses and summarizes some results on complex variables that are very useful in fractional-order systems analysis and design, specifically when the system is analyzed in the frequency domain. The author hopes that this…

We introduce a notion of refinements in the context of patching, in order to obtain new results about local-global principles and field invariants in the context of quadratic forms and central simple algebras. The fields we consider are…

We define and study a noncommutative Fourier transform on every homogeneous complex bounded domain. We then give an application in noncommutative differential geometry by defining noncommutative Baumslag-Solitar tori.

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,…

This paper examines the existence and region of convergence of Fourier transform of the functions of bicomplex variables with the help of projection on its idempotent components as auxiliary complex planes. Several basic properties of this…