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Inequalities play a fundamental role in Functional Analysis and it
is widely recognized that finding them, especially sharp estimates,
is an art. E. H. Lieb has discovered a host of inequalities that
are enormously useful in mathematics as well as in physics. His
results are collected in this book which should become a standard
source for further research. Together with the mathematical proofs
the author also presents numerous applications to the calculus of
variations and to many problems of quantum physics, in particular
to atomic physics.
Inequalities play a fundamental role in Functional Analysis and it is widely recognized that finding them, especially sharp estimates, is an art. E. H. Lieb has discovered a host of inequalities that are enormously useful in mathematics as well as in physics. His results are collected in this book which should become a standard source for further research. Together with the mathematical proofs the author also presents numerous applications to the calculus of variations and to many problems of quantum physics, in particular to atomic physics.
Significantly revised and expanded, this second edition provides
readers at all levels - from beginning students to practising
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. The authors quickly move from basic
topics, to methods that work successfully in mathematics and its
applications. While omitting many usual typical textbook topics,
this volume 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, and these should give the beginner a
sense that the subject is alive and growing.
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