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Title: Analysis by Elliott H. Lieb, Michael Loss ISBN: 0-8218-2783-9 Publisher: American Mathematical Society Pub. Date: 01 April, 2001 Format: Hardcover Volumes: 1 List Price(USD): $39.00 |
Average Customer Rating: 5 (2 reviews)
Rating: 5
Summary: A start in analysis.
Comment: 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.
Rating: 5
Summary: An excellent course of analysis with a theme
Comment: By the end of the sixties Dyson and Lennard, for the first time, proved that matter is stable. More precisely, they proved the thermodynamic stability of Coulomb matter. This was a landmark of mathematical physics, and a huge one: a very long and hard paper. A few years later, Elliott Lieb and Walter Thirring substantially improved the great Dyson result, dramatically cutting its length while improving important estimates. A very good review of these results can be find in the volume 4 of Thirring's "A Course in Mathematical Physics". Even the book version is a bit hard to read, as much mathematical analysis is required. The "Analysis" of Lieb and Loss is a book on analysis which has as a theme the great result of Lieb and Thirring. It is a real book on analysis. The chapters are named "Measure and Integration", "Lp-spaces","The Fourier transform", "Distributions", but also "Potential Theory and Coulomb En! ergies" and "Introduction to the Calculus of Variations", where nothing less than the Thomas-Fermi atom is rigorously studied. In order to leave no doubt that hard analysis is present, there are two chapters on Inequalities. After studying this splendid text the reader will be a better analist and, if he cares to, can start reading the proof of stability of matter. The proof of the pudding is NOT in the eating!
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Title: Counterexamples in Analysis by Bernard R. Gelbaum, John M. H. Olmsted ISBN: 0486428753 Publisher: Dover Pubns Pub. Date: 04 June, 2003 List Price(USD): $14.95 |
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Title: Measure and Integral by Richard Wheeden, Antoni Zygmund ISBN: 0824764994 Publisher: Marcel Dekker Pub. Date: 01 November, 1977 List Price(USD): $59.75 |
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Title: Real and Complex Analysis by Walter Rudin ISBN: 0070542341 Publisher: McGraw-Hill Science/Engineering/Math Pub. Date: 01 May, 1986 List Price(USD): $142.00 |
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Title: Elements of the Theory of Functions and Functional Analysis by A. N. Kolmogorov, S. V. Fomin ISBN: 0486406830 Publisher: Dover Pubns Pub. Date: 17 February, 1999 List Price(USD): $12.95 |
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Title: Introductory Real Analysis by A. N. Kolmogorov, S. V. Fomin ISBN: 0486612260 Publisher: Dover Pubns Pub. Date: 01 June, 1975 List Price(USD): $15.95 |
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