Convex functional analysis
type: Item
instance of: scholarly article
title: Convex functional analysis
zbMATH Open document ID: 1077.46002
author: A. J. Kurdila
author: Michael Zabarankin
published in: Systems \& Control: Foundations \& Applications
publication date: 2005-06-08T00:00:00Z
review text: This is the first of two volumes which are devoted to convex functional analysis and its application to contact problems in mechanics, shape optimization problems, identification problems in mechanics and control of incompressible flow. It is devoted to the fundamentals of convex functional analysis. It presents those aspects of functional analysis that are used in various applications to mechanics and control theory. The book provides not only the bare minimum of the theory required to understand the principles of functional, convex and set-valued analysis, but also a concise summary of definitions and theorems so that the text is self-contained. The contents includes an overview of classical abstract spaces (chapter 1), linear functionals and linear operators (chapter 2), common function spaces (Sobolev and Banach) (chapter 3), differential calculus in normed vector spaces (chapter 4), minimization functionals (chapter 5) and convex functionals (chapter 6), lower semicontinuous functionals (chapter 7). This book will be useful for those with a background in graduate mathematics who are interested in a concise summary of the main definitions and theorems in convex functional analysis.
reviewed by: Anatoliy Swishchuk
Mathematics Subject Classification ID: 46-01
Mathematics Subject Classification ID: 46N10
Mathematics Subject Classification ID: 49J27
Mathematics Subject Classification ID: 49J50
Mathematics Subject Classification ID: 49K27
Mathematics Subject Classification ID: 93C25
zbMATH DE Number: 2174320
zbMATH Keywords: topological and normed vector spaces
zbMATH Keywords: measure
zbMATH Keywords: integration
zbMATH Keywords: Hilbert and Sobolev spaces
zbMATH Keywords: linear operators
zbMATH Keywords: weak topologies
zbMATH Keywords: Gâteaux and Fréchet differentials
zbMATH Keywords: Lagrange multipliers
zbMATH Keywords: convex analysis
zbMATH Keywords: semicontinuous functionals
zbMATH Keywords: Weierstrass theorem
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2174320