Subdifferentials of convex symmetric functions: An application of the inequality of Hardy, Littlewood, and Pólya
type: Item
instance of: scholarly article
title: Subdifferentials of convex symmetric functions: An application of the inequality of Hardy, Littlewood, and Pólya
zbMATH Open document ID: 0668.46012
DOI: 10.1016/0022-247X(88)90167-9
author: Anthony Horsley
author: Andrew J. Wrobel
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46G05
Mathematics Subject Classification ID: 46A55
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 91B50
Mathematics Subject Classification ID: 26D10
zbMATH DE Number: 4094155
zbMATH Keywords: rearrangement-invariant function spaces
zbMATH Keywords: subgradient of a convex Schur function
zbMATH Keywords: subdifferential
zbMATH Keywords: basic convex Schur function
zbMATH Keywords: weakly lower semicontinuous convex Schur function
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4094155