Generic Fréchet differentiability of the pressure in certain lattice systems
type: Item
instance of: scholarly article
title: Generic Fréchet differentiability of the pressure in certain lattice systems
zbMATH Open document ID: 0537.46039
DOI: 10.1007/BF01206022
published in: Communications in Mathematical Physics
publication date: 1983-01-01T00:00:00Z
review text: This note has two goals. The first is to give an explicit description (Theorem 1) of the duals of certain weighted products \({\mathcal B}_ h\) of a countable family of Banach spaces. These products include the usual spaces of interactions which arise in statistical mechanics. The second goal is to use this description to prove that if the factor spaces are finite dimensional and the weight function h satisfies a certain growth condition, then the pressure is Fréchet differentiable wherever it is Gateaux differentiable (hence is Fréchet differentiable in a dense \(G_{\delta}\) subset).
Mathematics Subject Classification ID: 46G05
Mathematics Subject Classification ID: 46M40
Mathematics Subject Classification ID: 82B05
zbMATH DE Number: 3853787
zbMATH Keywords: generic Fréchet differentiability of the pressure
zbMATH Keywords: lattice systems
zbMATH Keywords: weighted products of a countable family of Banach spaces
zbMATH Keywords: Gateaux differentiable
zbMATH Keywords: Fréchet differentiable in a dense \(G_{\delta}\) subset
author: R. R. Phelps
MaRDI profile type: Publication
cites work: Differentiability properties of the pressure in lattice systems
cites work: Q3946604
cites work: Some convexity questions arising in statistical mechanics.
cites work: Q5564295
full work available at URL: https://doi.org/10.1007/bf01206022
OpenAlex ID: W2015805816
description: scientific article; zbMATH DE number 3853787