Functional Analysis

by Peter D. Lax

Overview

• Includes sections on the spectral resolution and spectral representation of self adjoint operators, invariant subspaces, strongly continuous one-parameter semigroups, the index of operators, the trace formula of Lidskii, the Fredholm determinant, and more.
• Assumes prior knowledge of Naive set theory, linear algebra, point set topology, basic complex variable, and real variables.
• Includes an appendix on the Riesz representation theorem.

Product Details

ISBN-13:	9780471556046
Publisher:	Wiley
Publication date:	04/04/2002
Series:	Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts , #55
Pages:	608
Product dimensions:	6.10(w) x 9.40(h) x 1.60(d)

About the Author

Peter D. Lax is a Series Advisor for the Wiley Interscience Series in Pure and Applied Mathematics. He is a professor of mathematics at the Courant Institute, the director of the Mathematics and computing Laboratory, and was director of the Institute from 1971 to 1980.

Table of Contents

Foreword.

Linear Spaces.

Linear Maps.

The Hahn-Banach Theorem.

Applications of the Hahn-Banach Theorem.

Normed Linear Spaces.

Hilbert Space.

Applications of Hilbert Space Results.

Duals of Normed Linear Space.

Applications of Duality.

Weak Convergence.

Applications of Weak Convergence.

The Weak and Weak* Topologies.

Locally Convex Topologies and the Krein-Milman Theorem.

Examples of Convex Sets and their Extreme Points.

Bounded Linear Maps.

Examples of Bounded Linear Maps.

Banach Algebras and their Elementary Spectral Theory.

Gelfand's Theory of Commutative Banach Algebras.

Applications of Gelfand's Theory of Commutative Banach Algebras.

Examples of Operators and their Spectra.

Compact Maps.

Examples of Compact Operators.

Positive Compact Operators.

Fredholm's Theory of Integral Equations.

Invariant Subspaces.

Harmonic Analysis on a Halfline.

Index Theory.

Compact Symmetric Operators in Hilbert Space.

Examples of Compact Symmetric Operators.

Trace Class and Trace Formula.

Spectral Theory of Symmetric, Normal and Unitary Operators.

Spectral Theory of Self-Adjoint Operators.

Examples of Self-Adjoint Operators.

Semigroups of Operators.

Groups of Unitary Operators.

Examples of Strongly Continuous Semigroups.

Scattering Theory.

A Theorem of Beurling.

Appendix A: The Riesz-Kakutani Representation Theorem.

Appendix B: Theory of Distributions.

Appendix C: Zorn's Lemma.

Author Index.

Subject Index.

Editorial Reviews

"...an excellent source of facts for anyone working in functional analysis or operator theory." (Journal of Operator Theory, Vol.53, No.1, 2005)

"For years Lax has been counted among the world's very top people in PDEs, so no serious student can afford to ignore his view of the foundations leading up to that subject." (Choice, Vol. 40, No. 4, December 2002)

"...attractive...well suited for graduate courses...and useful for research mathematicians." (Mathematical Reviews, 2003a)

"...The book is highly recommended to all students of analysis". (Zentralblatt MATH, Vol.1009, No.9, 2003)

"A lot of good material, doled out in short chapters." (American Mathematical Monthly, August/September 2003)

From the Publisher

Designed for a two-semester course at the graduate level, this text describes the theory and applications of functional analysis. In 38 short chapters, Lax (emeritus, mathematics, New York U.) addresses such topics as Banach spaces, weak sequential topologies, the Krein- Milman theorem, the Fredholm determinant, and scattering theory. Included in the appendices are a functional analytic proof of the Riesz-Kakutani representation theorem and an outline of the theory of distributions. Annotation c. Book News, Inc., Portland, OR (booknews.com)