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

  • A. Koldobsky
  • D. Ryabogin
  • Artem Zvavitch
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


A Fourier analytic approach to sections and projections of convex bodies has recently been developed and led to several results, including unified analytic solutions to the Busemann-Petty and Shephard problems, characterizations of intersection and projection bodies, extremal sections and projections of certain classes of bodies. The idea is to express certain geometric properties of convex bodies in terms of the Fourier transform, and then use methods of Fourier analysis to solve geometric problems. In this article, we outline the main features of this approach emphasizing similarities between results for sections and projections


Convex Body Intersection Body Symmetric Convex Body Projection Body Star Body 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • A. Koldobsky
    • 1
  • D. Ryabogin
    • 2
  • Artem Zvavitch
    • 3
  1. 1.Department of MathematicsUniversity of MissouriColumbiaUSA
  2. 2.Department of MathematicsKansas State UniversityManhattanUSA
  3. 3.Department of MathematicsKent State UniversityKentUSA

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