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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.
This volume contains the proceedings of the QMATH13: Mathematical
Results in Quantum Physics conference, held from October 8-11,
2016, at the Georgia Institute of Technology, Atlanta, Georgia. In
recent years, a number of new frontiers have opened in mathematical
physics, such as many-body localization and Schrodinger operators
on graphs. There has been progress in developing mathematical
techniques as well, notably in renormalization group methods and
the use of Lieb-Robinson bounds in various quantum models. The aim
of this volume is to provide an overview of some of these
developments. Topics include random Schrodinger operators,
many-body fermionic systems, atomic systems, effective equations,
and applications to quantum field theory. A number of articles are
devoted to the very active area of Schrodinger operators on graphs
and general spectral theory of Schrodinger operators. Some of the
articles are expository and can be read by an advanced graduate
student.
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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