Applied Functional Analysis: Main Principles and Their Applications

✍ Scribed by Eberhard Zeidler (auth.)

• Publisher: Springer-Verlag New York
• Year: 1995
• Tongue: English
• Leaves: 420
• Series: Applied Mathematical Sciences 109
• Edition: 1
• Category: Library

✦ Synopsis

A theory is the more impressive, the simpler are its premises, the more distinct are the things it connects, and the broader is its range of applicability. Albert Einstein There are two different ways of teaching mathematics, namely, (i) the systematic way, and (ii) the application-oriented way. More precisely, by (i), I mean a systematic presentation of the material governed by the desire for mathematical perfection and completeness of the results. In contrast to (i), approach (ii) starts out from the question "What are the most important applications?" and then tries to answer this question as quickly as possible. Here, one walks directly on the main road and does not wander into all the nice and interesting side roads. The present book is based on the second approach. It is addressed to undergraduate and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems that are related to our real world and that have played an important role in the history of mathematics. The reader should sense that the theory is being developed, not simply for its own sake, but for the effective solution of concrete problems. viii Preface Our introduction to applied functional analysis is divided into two parts: Part I: Applications to Mathematical Physics (AMS Vol. 108); Part II: Main Principles and Their Applications (AMS Vol. 109). A detailed discussion of the contents can be found in the preface to AMS Vol. 108.

✦ Table of Contents

Front Matter....Pages i-xvi
The Hahn-Banach Theorem and Optimization Problems....Pages 1-37
Variational Principles and Weak Convergence....Pages 39-165
Principles of Linear Functional Analysis....Pages 167-223
The Implicit Function Theorem....Pages 225-279
Fredholm Operators....Pages 281-370
Back Matter....Pages 371-406

✦ Subjects

Analysis; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization