Complex interpolation of R-norms, duality and foliations

被引：3

作者：

Berndtsson, Bo ^{[1
,2
]}

Cordero-Erausquin, Dario ^{[3
]}

Klartag, Bo'az ^{[4
,5
]}

Rubinstein, Yanir A. ^{[6
]}

机构：

[1] Chalmers Univ Technol, Gothenburg, Sweden

[2] Gothenburg Univ, Gothenburg, Sweden

[3] Sorbonne Univ, Inst Math Jussieu, Paris, France

[4] Weizmann Inst Sci, Tel Aviv, Israel

[5] Tel Aviv Univ, Tel Aviv, Israel

[6] Univ Maryland, College Pk, MD 20742 USA

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2020年 / 22卷 / 02期

基金：

美国国家科学基金会; 欧洲研究理事会;

关键词：

Complex interpolation; convex geometry; MONGE-AMPERE; POLYNOMIAL HULLS; BANACH-SPACES;

D O I：

10.4171/JEMS/927

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The complex method of interpolation, going back to Calderon 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-Ampere equation.

引用

页码：477 / 505

页数：29

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