MA 824 Functional Analysis (Spring 2012)

Mon and Thur 3:30 pm to 4.55 pm in Room 105

Informations about the course:

Content:

Review of normed linear spaces, Hahn-Banach theorems, duals, uniform boundedness principle, open mapping theorem, closed graph theorem, Riesz representation

theorem on Hilbert spaces, weak topologies, weak and weak* convergence, reflexivity in the setting of normed linear spaces, Compact operators,

Sturm-Liouville problems, spectral theorem for compact self adjoint operators, spectral projections, spectral decomposition theorem, spectral theorem

for a bounded normal operator.

Text/References:

1. J. B. Conway, Functional Analysis, 2nd Ed., Springer-Verlag, 1990.

2. I. Gohberg and S. Goldberg, Basic Operator Theory, Birkhäuser, 1980.

3. B. V. Limaye, Functional Analysis, 2nd Ed., New Age International Publishers, 1996.

4. M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 1: Functional Analysis, 2nd Ed., Academic Press, 1980.

5. W. Rudin, Functional Analysis, Tata McGraw Hill, 1974.

6. V. S. Sunder, Functional analysis- Spectral theory, TRIM, Hindustan Book Agency, 1997.

7. K. Yosida, Functional Analysis, 5th Ed., Narosa, 1979.

MA 824 Functional Analysis (Spring 2012)

Assignments