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Birkhäuser

Convex Functional Analysis

  • Textbook
  • © 2005

Overview

Authors:
  1. Andrew J. Kurdila

    1. Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Michael Zabarankin

    1. Department of Mathematical Sciences Stevens Institute of Technology, Castle Point on Hudson, Hoboken, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Intends to close the gap between theory and practice
  • Extends application of variational principles to recent problems in mechanics and control
  • Discusses the existence and development of solutions to these problems in the framework of convex functional analysis
  • Includes supplementary material: sn.pub/extras

Part of the book series: Systems & Control: Foundations & Applications (SCFA)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Classical Abstract Spaces in Functional Analysis

    Pages 1-62

  3. Linear Functionals and Linear Operators

    Pages 63-109

  4. Common Function Spaces in Applications

    Pages 111-136

  5. Differential Calculus in Normed Vector Spaces

    Pages 137-159

  6. Minimization of Functionals

    Pages 161-174

  7. Convex Functionals

    Pages 175-204

  8. Lower Semicontinuous Functionals

    Pages 205-219

  9. Back Matter

    Pages 221-228
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Keywords

About this book

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.

Reviews

"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 

Authors and Affiliations

  • Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, USA

    Andrew J. Kurdila

  • Department of Mathematical Sciences Stevens Institute of Technology, Castle Point on Hudson, Hoboken, USA

    Michael Zabarankin

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