Complex interpolation of R-norms, duality and foliations

Bo Berndtsson; Dario Cordero-Erausquin; Bo'az Klartag; Yanir A. Rubinstein

doi:10.4171/JEMS/927

Complex interpolation of R-norms, duality and foliations

Bo Berndtsson, Dario Cordero-Erausquin, Bo'az Klartag, Yanir A. Rubinstein

Weizmann Institute of Science, Tel Aviv University

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

Abstract

The complex method of interpolation, going back to Calderón and Coifman et al., on the one hand, and the Alexander-Wermer-Slodkowski theorem on polynomial hulls with convex fibers, on the other hand, are generalized to a method of interpolation of real (finite-dimensional) Banach spaces and of convex functions. The underlying duality in this method is given by the Legendre transform. Our results can also be interpreted as new properties of solutions of the homogeneous complex Monge-Ampère equation.

Original language	English
Pages (from-to)	477-505
Number of pages	29
Journal	Journal of the European Mathematical Society
Volume	22
Issue number	2
Early online date	29 Oct 2019
DOIs	https://doi.org/10.4171/JEMS/927
State	Published - 2020

Keywords

Complex interpolation
Convex geometry

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.4171/JEMS/927

https://arxiv.org/abs/1607.06306v2License: Other

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title = "Complex interpolation of R-norms, duality and foliations",

abstract = "The complex method of interpolation, going back to Calder{\'o}n and Coifman et al., on the one hand, and the Alexander-Wermer-Slodkowski theorem on polynomial hulls with convex fibers, on the other hand, are generalized to a method of interpolation of real (finite-dimensional) Banach spaces and of convex functions. The underlying duality in this method is given by the Legendre transform. Our results can also be interpreted as new properties of solutions of the homogeneous complex Monge-Amp{\`e}re equation.",

keywords = "Complex interpolation, Convex geometry",

author = "Bo Berndtsson and Dario Cordero-Erausquin and Bo'az Klartag and Rubinstein, \{Yanir A.\}",

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doi = "10.4171/JEMS/927",

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AU - Berndtsson, Bo

AU - Cordero-Erausquin, Dario

AU - Klartag, Bo'az

AU - Rubinstein, Yanir A.

PY - 2020

Y1 - 2020

N2 - The complex method of interpolation, going back to Calderón and Coifman et al., on the one hand, and the Alexander-Wermer-Slodkowski theorem on polynomial hulls with convex fibers, on the other hand, are generalized to a method of interpolation of real (finite-dimensional) Banach spaces and of convex functions. The underlying duality in this method is given by the Legendre transform. Our results can also be interpreted as new properties of solutions of the homogeneous complex Monge-Ampère equation.

AB - The complex method of interpolation, going back to Calderón and Coifman et al., on the one hand, and the Alexander-Wermer-Slodkowski theorem on polynomial hulls with convex fibers, on the other hand, are generalized to a method of interpolation of real (finite-dimensional) Banach spaces and of convex functions. The underlying duality in this method is given by the Legendre transform. Our results can also be interpreted as new properties of solutions of the homogeneous complex Monge-Ampère equation.

KW - Complex interpolation

KW - Convex geometry

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DO - 10.4171/JEMS/927

M3 - مقالة

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EP - 505

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

IS - 2

ER -

Complex interpolation of R-norms, duality and foliations

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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