Customer Reviews

I: Functional Analysis, Volume 1 (Methods of Modern Mathematical Physics) (vol 1)

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Books on mathematical methods "for physicists" are often criticized by their superficiality, a sacrifice deemed necessary for achieving completeness. This one is a glaring exception: the first of a set of 4 (!) volumes dealing with the finest tools for dealing with the delicate mathematical questions in quantum theory - namely, functional analysis. Of course, this sounds rather vague, since quantum physics makes use of functional-analytic tools as diverse as distributions, Hilbert, Banach and locally convex spaces, spectral theory, semigroup theory, operator algebras, etc.

However, do not expect ready-brew formulae and cookbook recipes: this book gets his job done at least as well as Rudin, Yosida and Riesz-Sz.Nagy, just to mention the classics. Most theorems are rigorously proved, and although the book becomes more and more biased towards mathematical physics (i.e., methods for proving self-adjointness, analysis of spectra and scattering theory, as stated in the section "Three Mathematical Problems in Quantum Mechanics". These methods occupy most of the three remaining volumes) as it proceeds - this bias becomes the true reason of being for the last two volumes - this particular volume has precisely the most useful stuff: metric, Banach, topological, locally convex, and Hilbert spaces, bounded and unbounded operators. A supplement extracted from the second volume with the basics of Fourier transforms makes it self-contained as a monograph.

However, the best things, that make this book nearly unbeatable, are the several wisely chosen examples and counterexamples, the notes at the end of each chapter and the wonderful - and useful - exercises. Many working mathematicians I know use this book seriously in their research and their courses in Functional Analysis - a fact that cannot be underestimated and will hardly be equaled by any book on mathematical physics.

If you work on (axiomatic) quantum field theory you may also want to keep an eye on the second volume of the set, "Fourier Analysis, Self-adjointness", which is a bit more specialized but just as wonderful.

We used this book in Math 401 at Princeton. This book is great, well-written, well-problemed. It is curious that the other reviewer complains that there is nothing original in this book, because this subject is older than the author, who is an expert in Schrodinger operators. The parts of the next three volumes which I have read have also been great.

This superb book may be the best available text on elementary general topology, functional analysis and spectral theory of bounded normal operators on Hilbert spaces. The exercises are excellent as well. Must reading!

This is an excellent text on functional analysis. I read a few books through the library when learning the subject and really loved the clarity of Reed-Simon the most. Also, the exercises are great.

However, the actual book that I received felt almost like photocopy quality and was difficult to read. The whole point of purchasing such an expensive text is to have it in your hands without the strain of staring at a computer screen. Elsevier did a downright crappy job with the new version (not the old maroon one).

This is the best functional analysis book for beginners, in my opinion. It is written for people that are interested in functional analysis as a tool for differential equations. What makes it different from other books on this subject are the numerous examples and applications to differential equations. Highly recommended.

Fast delivery, newer edition than what was advertised but that's perfectly fine with me

This books is an exposition to hilbert space theory. It contains a demonstration of the spectral theorem.

It is a deceiving book: while clearly written, there is nothing original in it.