Analysis (Graduate Studies in Mathematics)

Hardcover

ISBN 10: 0821827839 ISBN 13: 9780821827833

Publisher: American Mathematical Society, 2001

Significantly revised and expanded, this new Second Edition provides readers at all levels---from beginning students to practicing analysts---with the basic concepts and standard tools necessary to solve problems of analysis, and how to apply these concepts to research in a variety of areas.

Authors Elliott Lieb and Michael Loss take you quickly from basic topics to methods that work successfully in mathematics and its applications. While omitting many usual typical textbook topics, Analysis includes all necessary definitions, proofs, explanations, examples, and exercises to bring the reader to an advanced level of understanding with a minimum of fuss, and, at the same time, doing so in a rigorous and pedagogical way. Many topics that are useful and important, but usually left to advanced monographs, are presented in Analysis, and these give the beginner a sense that the subject is alive and growing.

This new Second Edition incorporates numerous changes since the publication of the original 1997 edition and includes:

Features:

a new chapter on eigenvalues that covers the min-max principle, semi-classical approximation, coherent states, Lieb-Thirring inequalities, and more

extensive additions to chapters covering Sobolev Inequalities, including the Nash and Log Sobolev inequalities

new material on Measure and Integration

many new exercises

and much more ...

The Second Edition continues its no-nonsense approach to the topic that has made it one of the best selling books on the subject. It is an authoritative, straight-forward volume that readers---from the graduate student, to the professional mathematician, to the physicist or engineer using analytical methods---will find useful both as a reference and as a guide to real problem solving.

About the authors: Elliott Lieb is Professor of Mathematics and Physics at Princeton University and is a member of the US, Austrian, and Danish Academies of Science. He is also the recipient of several prizes including the 1988 AMS/SIAM Birkhoff Prize. Michael Loss is Professor of Mathematics at the Georgia Institute of Technology.

From the Publisher:

This is an excellent course in operator theory and operator algebras ... leads the reader to deep new results and modern research topics ... the author has done more than just write a good book--he has managed to reveal the unspeakable charm of the subject, which is indeed the "source of happiness" for operator theorists.
-- Mathematical Reviews

Review:

"Begins with a down-to-earth intro ... aims at a side range of essential applications ... The book should work equally well in a one, or in a two semester course ... great for students to have ... This choice of book is also especially agreeable to grad students in physics who need to read up on the tools of analysis." ---- Palle Jorgensen

Praise for the previous edition ... "I find the selection of the material covered in the book very attractive and I recommend the book to anybody who wants to learn about classical as well as modern mathematical analysis." ---- European Mathematical Society Newsletter

"The essentials of modern analysis ... are presented in a rigorous and pedagogical way ... readers ... are guided to a level where they can read the current literature with understanding ... treatment of the subject is as direct as possible." ---- Zentralblatt MATH