Complex interpolation of R-norms, duality and foliations

• 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.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

Complex interpolation

convex geometry

monge-ampere

polynomial hulls

banach-spaces

Mathematics

Publication and Content Type

ref (subject category)

art (subject category)