Title | Fourier Analysis and Convexity [electronic resource] / edited by Luca Brandolini, Leonardo Colzani, Giancarlo Travaglini, Alex Iosevich |
---|---|

Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2004 |

Connect to | http://dx.doi.org/10.1007/978-0-8176-8172-2 |

Descript | IX, 268 p. online resource |

SUMMARY

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

CONTENT

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

Mathematics
Harmonic analysis
Fourier analysis
Functional analysis
Convex geometry
Discrete geometry
Number theory
Mathematics
Fourier Analysis
Abstract Harmonic Analysis
Convex and Discrete Geometry
Number Theory
Functional Analysis