Functional Analysis (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts) [Hardcover]

Peter D. Lax (Author)

Book Description

ISBN-10: 0471556041 | ISBN-13: 978-0471556046 | Publication Date: April 4, 2002 | Edition: 1

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.

Editorial Reviews

Review

“…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)

Product Details

• Hardcover: 608 pages
• Publisher: Wiley-Interscience; 1 edition (April 4, 2002)
• Language: English
• ISBN-10: 0471556041
• ISBN-13: 978-0471556046
• Product Dimensions: 6.5 x 1.5 x 9.3 inches
• Shipping Weight: 2.1 pounds (View shipping rates and policies)
• Average Customer Review: 4.4 out of 5 stars  See all reviews (8 customer reviews)
• Amazon Best Sellers Rank: #326,138 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

37 of 42 people found the following review helpful:

5.0 out of 5 stars Brings the subject to life!, August 1, 2002

By 

Palle E T Jorgensen "Palle Jorgensen" (Iowa City, Iowa United States) - See all my reviews
(VINE VOICE)    (REAL NAME)   

This review is from: Functional Analysis (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts) (Hardcover)

The subject of functional analysis, while fundamental and central in the landscape of mathematics, really started with
seminal theorems due to Banach, Hilbert, von Neumann, Herglotz, Hausdorff, Friedrichs, Steinhouse,...and many other of, the perhaps less well known, founding fathers, in Central Europe (at the time), in the period between the two World Wars. It gained from there because of its many sucess stories,- in proving new theorems, in unifying old ones, in offering a framework for

quantum theory, for dynamical systems, and for partial differential equations. The Journal of Functional Analysis, starting in the 1960ties, broadened the subject, reaching almost all branches of science, and finding functional analytic flavor
in theories surprisingly far from the original roots of the subject. Peter Lax has himself,-- alone and with others, shaped some of greatest successes of the period, right up to the present. That is in the book!! And it offers an upbeat outlook for the future. It has been tested in the class room,-it is really user-friendly. At the end of each chapter P Lax ofers personal recollections;-- little known stories of how several of the pioneers in the subject have been victims,- in the 30ties and the 40ties, of Nazi atrocities. The writing is crisp and engaged,- the exercises are great;- just
right for students to learn from. This is the book to teach from.

15 of 17 people found the following review helpful:

5.0 out of 5 stars Functional analysis, February 22, 2006

By 

Wolf Kohn (Seattle WA.) - See all my reviews
(REAL NAME)   

Amazon Verified Purchase

This review is from: Functional Analysis (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts) (Hardcover)

This is a very elegant text. The analysis theorems and proofs are well explained and connected with operator theory. The exercises are well chosen to further the reader's understanding of the subject.
I strongly recommend this book both as a class text and as a refence volume.

4 of 4 people found the following review helpful:

5.0 out of 5 stars Magic of the classroom, May 31, 2010

By 

G. Jennings (Houston Texas) - See all my reviews
(REAL NAME)   

This review is from: Functional Analysis (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts) (Hardcover)

Peter Lax leaves the magic of the mathematics, and his understanding thereof, in plain view. The author preserves in his written words the enthusiasm for mathematics that he has in the classroom. The book though permits the reader to proceed as his time permits as the results are set out in a number of brief chapters each of which has something of significance for the reader. This book should be of interest even to the expert who knows the results but who likes to read carefully crafted prose and who would like to understand some of the author's views about the way to think about mathematics. It is well worth the effort.