Scattering theory for unitary operators

Class dates :
April 12, 19, 26
May 10, 17, 24, 31
June 7, 14, 21, 28
July 5, 12, 19

Program :
0) Motivation
1) Hilbert space and linear operators
2) Spectral theory for unitary operators
3) Scattering theory
4) Scattering operator

For the evaluation, you need to submit the solutions of some exercises and/or the proofs of some statements. These submissions can take place at any time during the semester. If you have any question, contact me.

Works submitted by students :
Partial isometries and wave operators, by Hyuga Ito
Hilbert space and linear operators, ideals in B(H), general linear operators, by So Moriki
Cayley transform, Parseval's identity for vector valued functions, Vitali's convergence theorem, by So Moriki
Decomposability of scattering operator, by Hyuga Ito

References : (electronic version available upon request)
W. Amrein, Hilbert space methods in quantum mechanics, EPFL press, 2009.
W. Amrein, Non-relativistic Quantum dynamics, Reidel Publishing Company, 1981.
W. Amrein, A. Boutet de Monvel, V. Georgescu, Co-groups, commutator methods and spectral theory of N-body Hamiltonians, Birkhauser, 1996.
H. Baumgartel, M. Wollenberg, Mathematical scattering theory, Birkhauser, 1983.
T. Kato, Perturbation theory for linear operators, Springer, 1995.
T. Kato, S.T. Kuroda, Theory of simple scattering and eigenfunction expansions, Functional Analysis and Related Fields (Proc. Conf. for M. Stone, Univ. Chicago, Chicago, Ill., 1968) pp. 99-131. Springer, New York, 1970.
G. Murpy, C*-algebras and operator theory, Academic Press, 1990.
J. Weidmann, Linear operators in Hilbert spaces, Springer, 1980.
D. Yafaev, Mathematical scattering theory: general theory, AMS, 1992.
D. Yafaev, Mathematical scattering theory: analytic theory, AMS, 2010.