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An Entity of Type : rdac:C10001, within Data Space : data.idref.fr associated with source document(s)

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type
Author
dc:subject
  • Géométrie convexe
  • Banach spaces
  • Banach, Espaces de
  • Fourier, Opérateurs intégraux de
  • Fourier, Transformations de
  • Fourier transformations
  • Convex sets
  • Ensembles convexes
preferred label
  • Fourier analysis in convex geometry
Language
Subject
dc:title
  • Fourier analysis in convex geometry
note
  • 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 method to solve geometric problems. One of the results discussed in the book is Ball’s theorem, establishing the exact upper bound for the (n-1)-dimensional volume of hyperplane sections of the n-dimensional unit cube (it is √2 for each n ≥ 2). Another is the Busemann-Petty problem: if K and L are two convex origin-symmetric n-dimensional bodies and the (n – 1)-dimensional volume of each central hyperplane section of K is less than the (n – 1)-dimensional volume of the corresponding section of L, is it true that the n-dimensional volume of K is less than the volume of L? (The answer is positive for n≤4 and negative for n>4). The book is suitable for all mathematicians interested in geometry, harmonic and functional analysis, and probability. Prerequisites for reading this book includes basic real, complex, and functional analysis.
dc:type
  • Text
http://iflastandar...bd/elements/P1001
rdaw:P10219
  • 2005
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