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Analysis (Graduate Studies in Mathematics) Hardcover – 30 Mar 2001


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Amazon.com: HASH(0x9f8d4190) out of 5 stars 5 reviews
31 of 32 people found the following review helpful
HASH(0x9bbeb6b4) out of 5 stars A start in analysis. 5 Jan. 2003
By Palle E T Jorgensen - Published on Amazon.com
Format: Hardcover
A start in analysis.-- For some number of years, Rudin's "Real and Complex", and a few other analysis books, served as the canonical choice for the book to use, and to teach from, in a first year grad analysis course. Lieb-Loss offers a refreshing alternative: It begins with a down-to-earth intro to measure theory, L^p and all that...It aims at a wide range of essential applications, such as the Fourier transform, and series, inequalities, distributions, and Sobolev spaces,--- PDE, potential theory, calculus of variations, and math physics (Schrodinger's equation, the hydrogen atom, Thomas-Fermi theory... to mention a few.) The book should work equallly well in a one, or in a two semester course. The first half of the book covers the basics, and the rest will be great for students to have, regardless of whether or not it gets to be included in a course. This choice of book is also especially agreeable to grad students in physics who need to read up on the tools of analysis.
19 of 20 people found the following review helpful
HASH(0x9ba2f39c) out of 5 stars A tremendous jumpstart into modern mathematical physics 12 May 2010
By J. R. G. Mendonca - Published on Amazon.com
Format: Hardcover Verified Purchase
I am a physicist with a somewhat limited mathematical background. However, I decided to 'break in' in modern mathematical physics, and that meant acquiring first a modicum of functional analysis and the required measure theory, harmonic analysis, and operator theory that goes with it. If you can afford the time, the classical learning path through, e.g., Kolmogorov & Fomin > Rudin (R&C) > Reed & Simon I (a path that I recommend, by the way), with possible excursions into ODEs and PDEs, probability theory, and modern geometry, is the safe way to go. If you cannot afford the time, read Lieb & Loss. It provides a tremendous jump start into what really matters for a beginning mathematical physicist: a little measure theory, L^p spaces, Sobolev spaces, a bit of Fourier analysis and PDEs, and inequalities -- lots of them (integral, Sobolev, variational). The main theorems are stated, most with proofs, and put into use.

I had a mathematical physics teacher in graduate school that once said (somewhat half-jokingly) that all you need to know is the monotone and dominated convergence theorems, the Fubini theorem, the Borel-Cantelli lemma, the Euler-Lagrange equations and how to resolve the identity using plane waves. This book by Lieb & Loss is a testimony to his confession.
HASH(0x9ba30aa4) out of 5 stars Good book 23 May 2016
By Guixiang Xu - Published on Amazon.com
Format: Hardcover Verified Purchase
It is an excellent book, I like it.
0 of 3 people found the following review helpful
HASH(0x9bbeb6fc) out of 5 stars Four Stars 19 Nov. 2015
By kader - Published on Amazon.com
Format: Hardcover Verified Purchase
I am satisfied
0 of 10 people found the following review helpful
HASH(0x9ba2f390) out of 5 stars Five Stars 21 Oct. 2014
By Gaetano - Published on Amazon.com
Format: Hardcover
Very good
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