ψ2-Estimate for the Euclidean Norm on a Convex Body in Isotropic Position

  • Simeon Alesker
Part of the Operator Theory Advances and Applications book series (OT, volume 77)


Let ℝ n be the n-dimensional euclidean space with fixed scalar product (·,·) and the norm |x|2 = (x, x). Denote D n = {x ∈ ℝ n | |x| ≤ 1} the unit euclidean ball, |A| = vol n A the Lebesgue n-dimensional measure. Let K be compact convex body in \( \mathbb{R}^n ,b = \frac{1} {{|K|}}\int_K {xdx} \) be its centroid and \(M = (m_{ij} )_{i,j = 1}^n \) be the matrix of inertia of K with entries \( m_{ij} = \frac{1} {{|K|}}\int_K {x_i x} _j dx.\)


Convex Body Absolute Constant Isoperimetric Problem Entry Operator Sackler Faculty 
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Copyright information

© Birkhäuser Verlag Basel/Switzerland 1995

Authors and Affiliations

  • Simeon Alesker
    • 1
  1. 1.Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael

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