Fourier Analysis and Convexity

  • Luca Brandolini
  • Leonardo Colzani
  • Giancarlo Travaglini
  • Alex Iosevich

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

About this book

Introduction

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 volume is dedicated to Fourier analysis, convex geometry, and related topics. Specific topics covered include:

* the geometric properties of convex bodies

* the study of Radon transforms

* the geometry of numbers

* the study of translational tilings using Fourier analysis

* irregularities in distributions

* Lattice point problems examined in the context of number theory, probability theory, and Fourier analysis

* restriction problems for the Fourier transform  

The 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.

Contributors: J. Beck, C. Berenstein, W.W.L. Chen, B. Green, H. Groemer, A. Koldobsky, M. Kolountzakis, A. Magyar, A.N. Podkorytov, B. Rubin, D. Ryabogin, T. Tao, G. Travaglini, A. Zvavitch

Keywords

Fourier transform calculus distribution functional analysis harmonic analysis linear optimization number theory

Editors and affiliations

  • Luca Brandolini
    • 1
  • Leonardo Colzani
    • 2
  • Giancarlo Travaglini
    • 2
  • Alex Iosevich
    • 3
  1. 1.Dipartimento di Ingegneria Gestionale e dell’ InformazioneUniversità di BergamoDalmineItaly
  2. 2.Dipartimento di Matematica e ApplicazioniUniversità di Milano-BicoccaMilanoItaly
  3. 3.Department of MathematicsUniversity of Missouri-ColumbiaColumbiaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-8172-2
  • Copyright Information Springer Science+Business Media New York 2004
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6474-3
  • Online ISBN 978-0-8176-8172-2
  • About this book
Industry Sectors
Aerospace