Elliott H. Lieb Princeton University, Princeton,
NJ, USA
Michael Loss, Georgia Institute of Technology,
Atlanta, GA, USA
This is an excellent textbook on analysis and it has several unique
features: Proofs of heat kernel estimates, the Nash inequality and
the logarithmic Sobolev inequality are topics that are seldom
treated on the level of a textbook. Best constants in several
inequalities, such as Young's inequality and the logarithmic
Sobolev inequality, are also included. A thorough treatment of
rearrangement inequalities and competing symmetries appears in book
form for the first time. There is an extensive treatment of
potential theory and its applications to quantum mechanics, which,
again, is unique at this level. Uniform convexity of Lp space is
treated very carefully. The presentation of this important subject
is highly unusual for a textbook. All the proofs provide deep
insights into the theorems. This book sets a new standard for a
graduate textbook in analysis." - Shing-Tung Yau
"Begins with a down-to-earth intro … aims at a wide 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
"Lieb and Loss offer a practical presentation of real and
functional analysis at the beginning graduate level … could be used
as a two-semester introduction to graduate analysis … not all of
the topics covered are typical. The authors introduce the subject
with a thorough presentation … [an] informative exposition." -
CHOICE
"This is definitely a beautiful book … useful reference even for
specialists since the authors present basic tools in a very
rigorous way … they show clever methods how to calculate, equally
useful for beginners as well as advanced specialists … well known
exercises." - Mathematica Bohemica
"Interesting textbook ... brings the reader quickly to a level
where a wide range of topics can be appreciated ... well-written
textbook ... can be read by anyone with a good knowledge of
calculus ... useful for graduate students in mathematics and
physics." - ZAMM–Journal of Applied Mathematics and Mechanics
"I liked the book very much. The topics chosen were suited toward
concepts that I wanted students to master." - Gary Sampson, Auburn
University
"In the area of analysis / real analysis / functional analysis
there are a very large number of books at all levels, many of them
very well known: the one under review is an unusual addition to the
list. The book by Lieb and Loss assumes little on the part of the
reader beyond a good college calculus course and, as such, begins
with the basics of Lebesgue integral and yet is able to go deep
into quite a few topics usually treated in advanced or more
specialised texts. This unorthodox development makes it possible
for a reader to reach, in the space of less than three hundred
pages, completely rigorous mathematical treatment of several
interesting physical problems. The authors have exercised
remarkable discipline in their choice of topics to reach such
depths quickly, yet they have not made it a linear development with
the sole aim of showing these applications... To sum up, this is an
excellent book and the present inexpensive edition is recommended
for the libraries of all interested in analysis." - Resonance:
Journal of Science Edition
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