Discretization and affine approximation in high dimensions

Sean Li; Assaf Naor

doi:10.1007/s11856-012-0182-1

Discretization and affine approximation in high dimensions

Sean Li
, Assaf Naor

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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 language	English (US)
Pages (from-to)	107-129
Number of pages	23
Journal	Israel Journal of Mathematics
Volume	197
Issue number	1
DOIs	https://doi.org/10.1007/s11856-012-0182-1
State	Published - Oct 2013
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s11856-012-0182-1

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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.",

author = "Sean Li and Assaf Naor",

note = "Funding Information: ∗S. L. was supported by NSF grant CCF-0832795. A. N. was supported by NSF grant CCF-0832795, BSF grant 2010021, and the Packard Foundation. Some of this work was completed when both authors were in residence at the MSRI Quantitative Geometry program. Received February 18, 2012 and in revised form May 9, 2012",

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AU - Naor, Assaf

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PY - 2013/10

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N2 - 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.

AB - 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.

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JO - Israel Journal of Mathematics

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Discretization and affine approximation in high dimensions

Abstract

All Science Journal Classification (ASJC) codes

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