Fourier Analysis in Convex Geometry

Released on by Alexander Koldobsky
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  • Fourier Analysis in Convex Geometry Book Detail

  • Author : Alexander Koldobsky
  • Release Date : 2014-11-12
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 178
  • ISBN 13 : 1470419521
  • File Size : 76,76 MB
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Fourier Analysis in Convex Geometry by Alexander Koldobsky PDF Summary

Book Description: The study of the geometry of convex bodies based on information about sections and projections of these bodies has important applications in many areas of mathematics and science. In this book, a new Fourier analysis approach is discussed. The idea is to express certain geometric properties of bodies in terms of Fourier analysis and to use harmonic analysis methods to solve geometric problems. One of the results discussed in the book is Ball's theorem, establishing the exact upper bound for the -dimensional volume of hyperplane sections of the -dimensional unit cube (it is for each ). Another is the Busemann-Petty problem: if and are two convex origin-symmetric -dimensional bodies and the -dimensional volume of each central hyperplane section of is less than the -dimensional volume of the corresponding section of , is it true that the -dimensional volume of is less than the volume of ? (The answer is positive for and negative for .) The book is suitable for graduate students and researchers interested in geometry, harmonic and functional analysis, and probability. Prerequisites for reading this book include basic real, complex, and functional analysis.

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Fourier Analysis in Convex Geometry

Fourier Analysis in Convex Geometry

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The study of the geometry of convex bodies based on information about sections and projections of these bodies has important applications in many areas of mathe

Fourier Analysis and Convexity

Fourier Analysis and Convexity

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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 ad