相关论文: Notes on harmonic analysis Part II: the Fourier Se…

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 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,…

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

The Fourier series method is used to solve the homogeneous equation governing the motion of the harmonic oscillator. It is shown that the general solution to the problem can be found in a surprisingly simple way for the case of the simple…

Mathematics is a far reaching discipline and its tools appear in many applications. In this paper we discuss its role in music and signal processing by revisiting the use of mathematics in algorithms that can extract chord information from…

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

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

Fourier analysis plays a major role in the analysis and understanding of many phenomena in physics and contemporary engineering. However, students, who have often discovered this notion through numerical tools, do not necessarily understand…

This is the material for two lectures given at Ecole Polytechnique in May 2011 for the math teachers of "classes pr\'eparatoires"(parallel to the undergraduate classes in universities). The introduction is a personal overview on Fourier…

We evaluate binomial series with harmonic number coefficients, providing recursion relations, integral representations, and several examples. The results are of interest to analytic number theory, the analysis of algorithms, and…

Extending ideas of A.N. Parshin and D.V. Osipov, Harmonic Analysis is developed for filtered infinite dimensional modules over a ring. We establish Pontryagin duality, the Fourier inversion formula, Plancherel formula and Poisson summation…

This book is an introduction to the nascent field of Fourier analysis on polytopes, and cones. There is a rapidly growing number of applications of these methods, so it is appropriate to invite students, as well as professionals, to the…

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 note gives a summary of ideas concerning Applied Fourier Analysis, mostly formulated for those who have to give such courses to engineers or mathematicians interested in real life applications. It tries to answer recurrent questions…

This is a survey of the use of Fourier analysis in additive combinatorics, with a particular focus on situations where it cannot be straightforwardly applied, but needs to be generalized first. Sometimes very satisfactory generalizations…

Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. The second paper is concerned with simultaneous approximation to functions and their…

Given a dilation matrix M, a so-called space of M-positive vectors in the Euclidean space is introduced and studied. An algebraic structure of this space is similar to the positive half-line equipped with the termwise addition modulo 2,…

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

A set of semi-analytical techniques based on Fourier analysis is used to solve wave scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are newly developed conformal mapping…

Applications of harmonic analysis on finite groups were recently introduced to measure partition problems, with a variety of equipartition types by convex fundamental domains obtained as the vanishing of prescribed Fourier transforms.…