Fourier Analysis and Convexity / Edition 1

by Luca Brandolini, Leonardo Colzani, Alex Iosevich, Giancarlo Travaglini

Overview

Over the course of the last century, the systematic exploration of the relationship between Fourier analysis and other branches of mathematics has lead to important advances in geometry, number theory, and analysis, stimulated in part by Hurwitz’s proof of the isoperimetric inequality using Fourier series.

This unified, self-contained book presents both a broad overview of Fourier analysis and convexity, as well as an intricate look at applications in some specific settings; it will be useful to graduate students and researchers in harmonic analysis, convex geometry, functional analysis, number theory, computer science, and combinatorial analysis. A wide audience will benefit from the careful demonstration of how Fourier analysis is used to distill the essence of many mathematical problems in a natural and elegant way.

Product Details

ISBN-13:	9780817632632
Publisher:	Birkhäuser Boston
Publication date:	08/06/2004
Series:	Applied and Numerical Harmonic Analysis
Edition description:	2004
Pages:	268
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

Lattice Point Problems: Crossroads of Number Theory, Probability Theory and Fourier Analysis.- Totally Geodesic Radon Transform of LP-Functions on Real Hyperbolic Space.- Fourier Techniques in the Theory of Irregularities of Point Distribution.- Spectral Structure of Sets of Integers.- 100 Years of Fourier Series and Spherical Harmonics in Convexity.- Fourier Analytic Methods in the Study of Projections and Sections of Convex Bodies.- The Study of Translational Tiling with Fourier Analysis.- Discrete Maximal Functions and Ergodic Theorems Related to Polynomials.- What Is It Possible to Say About an Asymptotic of the Fourier Transform of the Characteristic Function of a Two-dimensional Convex Body with Nonsmooth Boundary?.- SomeRecent Progress on the Restriction Conjecture.- Average Decayof the Fourier Transform.