TCC: Spectral and Functional Inequalities and their applications
Description of the course:
We shall start with some preliminary material describing basic concepts of self-adjoint operators in Hilbert Space such as compact, bounded and unbounded operators, semi-bounded operators and Friedrichs extensions, variational principle, Birman-Schwinger principle.
The course will include:
Lectures:Lectures - week 1
Problems:problem sheet 1
Mikhail S. Birman and Michael Z. Solomyak, Spectral Theory of self-adjoint operators in Hilbert Space D. Reidel Publishing House, 1987.
M. Reed and B. Simon, Methods of modern mathematical physics. IV: Analysis of Operators, Academic Press, 1978.
Elliott H. Lieb and Michael Loss, Analysis, American Mathematical Society; 2 edition, 2001.
Elliott H. Lieb and Robert Seiringer, The stability of matter in Quantum Mechanics, Cambridge University Press, 2009.
Vladimir Maz'ya, Sobolev Spaces, Springer, 2nd Edition., 2011.