Discretization and affine approximation in high dimensions

Sean Li, Assaf Naor

Research output: Contribution to journalArticle

Abstract

Lower estimates are obtained for the macroscopic scale of affine approximability of vector-valued Lipschitz functions on finite-dimensional normed spaces, completing the work of Bates, Johnson, Lindenstrauss, Preiss and Schechtman. This yields a new approach to Bourgain's discretization theorem for superreflexive targets.

Original languageEnglish (US)
Pages (from-to)107-129
Number of pages23
JournalIsrael Journal of Mathematics
Volume197
Issue number1
DOIs
StatePublished - Oct 2013

Fingerprint

Approximability
Lipschitz Function
Vector-valued Functions
Normed Space
Higher Dimensions
Discretization
Target
Approximation
Theorem
Estimate

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Discretization and affine approximation in high dimensions. / Li, Sean; Naor, Assaf.

In: Israel Journal of Mathematics, Vol. 197, No. 1, 10.2013, p. 107-129.

Research output: Contribution to journalArticle

Li, Sean ; Naor, Assaf. / Discretization and affine approximation in high dimensions. In: Israel Journal of Mathematics. 2013 ; Vol. 197, No. 1. pp. 107-129.
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