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1 results

  • 4 - Multivariate Christoffel–Darboux Analysis

  • from Part One - Historical and Theoretical Background
  • Jean Bernard Lasserre, Edouard Pauwels, Institut de Recherche en Informatique, Toulouse, Mihai Putinar, University of California, Santa Barbara
  • Book:
    The Christoffel–Darboux Kernel for Data Analysis
    Published online:
    31 March 2022
    Print publication:
    07 April 2022, pp 42-60

  • Summary

    Starting from the explicit formulas known for simple multivariate geometries (balls, cube, simplex) the discussion moves to recent advances in pluripotential theory. The essential Bernstein-Markov property of a measure is necessary for deriving asymptotics of the Christoffel function outside the support of the generating measure, and in some fortunate situations also inside the support. A balance between strong and weak limits enters into the game.