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

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Fourier Analysis and Convexity

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

Abstract

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

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Missouri, Columbia, MO, 65211, USA

    A. Koldobsky

  2. Department of Mathematics, Kansas State University, Manhattan, KS, 66506, USA

    D. Ryabogin

  3. Department of Mathematics, Kent State University, Kent, OH, 44442, USA

    Artem Zvavitch

Authors
  1. A. Koldobsky
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  2. D. Ryabogin
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  3. Artem Zvavitch
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Editor information

Editors and Affiliations

  1. Dipartimento di Ingegneria Gestionale e dell’ Informazione, Università di Bergamo, Dalmine, 24044, Italy

    Luca Brandolini

  2. Dipartimento di Matematica e Applicazioni, UniversitĂ  di Milano-Bicocca, Milano, 20126, Italy

    Leonardo Colzani  & Giancarlo Travaglini  & 

  3. Department of Mathematics, University of Missouri-Columbia, Columbia, MO, 65211, USA

    Alex Iosevich

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Koldobsky, A., Ryabogin, D., Zvavitch, A. (2004). Fourier Analytic Methods in the Study of Projections and Sections of Convex Bodies. In: Brandolini, L., Colzani, L., Travaglini, G., Iosevich, A. (eds) Fourier Analysis and Convexity. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8172-2_6

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  • DOI: https://doi.org/10.1007/978-0-8176-8172-2_6

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  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6474-3

  • Online ISBN: 978-0-8176-8172-2

  • eBook Packages: Springer Book Archive

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