Customer Reviews

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

5 star:		(6)
4 star:		(1)
3 star:		(0)
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1 star:		(1)

 

 

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.

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.

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.

This is a very good book, provided you belong to its target audience. Ideally, this means you are a grad student in math or applied math, with at least some basic knowledge in FA. I would not recommend it as a first book on the topic for someone who has never seen FA. But if you did pick up some FA along the way and now you want to take a step to the next level - this book would be a great choice.

The author also supplies important historical facts about how many of the great mathematicians in the field of FA were murdered by the Nazis (most, but not all, of them were Jewish). Now forget the math for a second; for this alone, the book is important.

This was the assigned text for an introductory graduate course in functional analysis I took. It is what we might call a very clean and elegant text of functional analysis. For the audience with the requisite mathematical maturity it will be a joy to read. For myself, I can see it's elegance, but do need a supplementary text to fill in some spaces for me. I found Bachman & Narici, and Kreyszig to be the supplements. This is a great book to have for reference, but it needs a real index.

The book makes the subject fun while covering a lot of material. The author is an excellent mathematician, and this shows through on every page. The historical asides are very informative (if depressing, since they all, by choice, since Lax writes about the generation which influenced him (and a lot of which perished in the concentration camps, a fate Lax narrowly escaped himself, as did another giant of functional analysis (of a rather different style) -- A. Grothendieck)

Peter D Lax is one of the great mathematicians of the 2nd half of the 20th century. Buy this book if only to have it on your bookshelf. After a long day of suffering fools and putting up with the latest insanities of your university administrators, leaf through Lax's book to recover. This is mathematics at its best. What better use can we put mathematics to, than to help us regain our sanity in a world that's gone mad.

This text is more suited as a review for someone
who already knows the results. There is very
little in the way of motivation for the various
definitions.