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Birkhäuser

Fourier Analysis and Convexity

  • Book
  • © 2004

Overview

Editors:
  1. Luca Brandolini

    1. Dipartimento di Ingegneria Gestionale e dell’ Informazione, Università di Bergamo, Dalmine, Italy

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  2. Leonardo Colzani

    1. Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Milano, Italy

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  3. Giancarlo Travaglini

    1. Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Milano, Italy

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  4. Alex Iosevich

    1. Department of Mathematics, University of Missouri-Columbia, Columbia, USA

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  • 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

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

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-ix
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  2. Lattice Point Problems: Crossroads of Number Theory, Probability Theory and Fourier Analysis

    • József Beck
    Pages 1-35

  3. Totally Geodesic Radon Transform of L p-Functions on Real Hyperbolic Space

    • Carlos A. Berenstein, Boris Rubin
    Pages 37-58

  4. Fourier Techniques in the Theory of Irregularities of Point Distribution

    • W. W. L. Chen
    Pages 59-82

  5. Spectral Structure of Sets of Integers

    • Ben Green
    Pages 83-96

  6. 100 Years of Fourier Series and Spherical Harmonics in Convexity

    • H. Groemer
    Pages 97-118

  7. Fourier Analytic Methods in the Study of Projections and Sections of Convex Bodies

    • A. Koldobsky, D. Ryabogin, Artem Zvavitch
    Pages 119-130

  8. The Study of Translational Tiling with Fourier Analysis

    • Mihail N. Kolountzakis
    Pages 131-187

  9. Discrete Maximal Functions and Ergodic Theorems Related to Polynomials

    • Akos Magyar
    Pages 189-208

  10. 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?

    • A. N. Podkorytov
    Pages 209-215

  11. Some Recent Progress on the Restriction Conjecture

    • Terence Tao
    Pages 217-243

  12. Average Decay of the Fourier Transform

    • Giancarlo Travaglini
    Pages 245-268
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Keywords

About this book

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.

Editors and Affiliations

  • Dipartimento di Ingegneria Gestionale e dell’ Informazione, Università di Bergamo, Dalmine, Italy

    Luca Brandolini

  • Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Milano, Italy

    Leonardo Colzani, Giancarlo Travaglini

  • Department of Mathematics, University of Missouri-Columbia, Columbia, USA

    Alex Iosevich

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