Complex interpolation of $\mathbb{R}$-norms, duality and foliations
Complex Variables
2024-11-25 v2 Functional Analysis
Abstract
The complex method of interpolation, going back to Calder\'on 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\`ere equation.
Cite
@article{arxiv.1607.06306,
title = {Complex interpolation of $\mathbb{R}$-norms, duality and foliations},
author = {Bo Berndtsson and Dario Cordero-Erausquin and Bo'az Klartag and Yanir A. Rubinstein},
journal= {arXiv preprint arXiv:1607.06306},
year = {2024}
}