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

  Klappentext

  Explores relationship between Fourier Analysis, convex geometry, and related areas; in the past, study of this relationship has led to important mathematical advances

  Presents new results and applications to diverse fields such as geometry, number theory, and analysis

  Contributors are leading experts in their respective fields

  Will be of interest to both pure and applied mathematicians