Convex Functional Analysis

ISBN-13: 9783764321987 / Angielski / Twarda / 2005 / 228 str.

Andrew J. Kurdila; Michael Zabarankin

Opis

Overview of Book This book evolved over a period of years as the authors taught classes in var- tional calculus and applied functional analysis to graduatestudents in engineering and mathematics. The book has likewise been in?uenced by the authors' research programs that have relied on the application of functional analytic principles to problems in variational calculus, mechanics and control theory. One of the most di?cult tasks in preparing to utilize functional, convex, and set-valued analysis in practical problems in engineering and physics is the inti- dating number of de?nitions, lemmas, theorems and propositions that constitute thefoundationsoffunctionalanalysis. Itcannotbeoveremphasizedthatfunctional analysis can be a powerful tool for analyzing practical problems in mechanics and physics. However, many academicians and researchers spend their lifetime stu- ing abstract mathematics. It is a demanding ?eld that requires discipline and devotion. It is a trite analogy that mathematics can be viewed as a pyramid of knowledge, that builds layer upon layer as more mathematical structure is put in place. The di?culty lies in the fact that an engineer or scientist typically would like to start somewhere "above the base" of the pyramid. Engineers and scientists are not as concerned, generally speaking, with the subtleties of deriving theorems axiomatically. Rather, they are interested in gaining a working knowledge of the applicability of the theory to their ?eld of interest.

Recenzje

"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."   -Zentralblatt MATH

"This book...is intended as a textbook for classes in variational calculus and applied functional analysis for graduate students in engineering and applied mathematics.... The book is the result of the courses taught by the authors through the years and tries to address the different backgrounds [that] different types of students come in with when taking these courses. The topics covered provide both a treatment of the theoretical aspects of functional analysis, as well as their applications to variational calculus, mechanics and control theory.... I am sure that many instructors seeking a textbook for a course on the applications of functional analysis for engineering or applied mathematics students will find this text very useful."   -MAA Reviews 

Spis treści

Classical Abstract Spaces in Functional Analysis.- Linear Functionals and Linear Operators.- Common Function Spaces in Applications.- Differential Calculus in Normed Vector Spaces.- Minimization of Functionals.- Convex Functionals.- Lower Semicontinuous Functionals.

Blurb

This volume is dedicated to the fundamentals of convex functional analysis. It presents those aspects of functional analysis that are extensively used in various applications to mechanics and control theory. The purpose of the text is essentially two-fold. On the one hand, a bare minimum of the theory required to understand the principles of functional, convex and set-valued analysis is presented. Numerous examples and diagrams provide as intuitive an explanation of the principles as possible. On the other hand, the volume is largely self-contained. Those with a background in graduate mathematics will find a concise summary of all main definitions and theorems.

Contents:
Classical Abstract Spaces in Functional Analysis
Linear Functionals and Linear Operators
Common Function Spaces in Applications
Differential Calculus in Normed Vector Spaces
Minimization of Functionals
Convex Functionals
Lower Semicontinuous Functionals