Subdifferentials of convex symmetric functions: An application of the inequality of Hardy, Littlewood, and Pólya
The authors consider Schur functions \(f:L^ p(\mu)\to {\mathbb{R}}\), where \(\mu\) is a nonatomic probability measure. They prove that any subgradient of a convex Schur function is ``arranged similarly'' to the point where it is taken, thus extending Schur's classical result for differentiable Schur functions on \({\mathbb{R}}^ n\). They go on to compute the subdifferential of the ``basic convex Schur function'', so called because any weakly lower semicontinuous convex Schur function can be written as the pointwise supremum of a family of its translates. This computation enables them to characterize the extreme points of certain subdifferential sets. References to the economic literature on electricity pricing and investment are given.
weakly lower semicontinuous convex Schur function
scientific article; zbMATH DE number 4094155