The analysis of eigenvalues of Laplace and Schroedinger operators
is an important and classical topic in mathematical physics with
many applications. This book presents a thorough introduction to
the area, suitable for masters and graduate students, and includes
an ample amount of background material on the spectral theory of
linear operators in Hilbert spaces and on Sobolev space theory. Of
particular interest is a family of inequalities by Lieb and
Thirring on eigenvalues of Schroedinger operators, which they used
in their proof of stability of matter. The final part of this book
is devoted to the active research on sharp constants in these
inequalities and contains state-of-the-art results, serving as a
reference for experts and as a starting point for further research.
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