MTMS 507

MTMS 507 : FUNCTIONAL ANALYSIS 4 Credits

1. Topological Linear Spaces: Convex sets and hyperplanes, seminorms, locally convex spaces, weak topology, compact convex sets, duality in Banach spaces.

2. Linear Operators: Continuity and boundedness, fundamental properties of bounded operators, uniform boundedness principle, conjugate of bounded linear operators, adjoint operator and its duality, bounded linear operators in Hilbert spaces, unbounded linear operator.

3. Spectral Analysis of Linear Operators: Spectrum and the resolvent operator, spectrum of a bounded linear operator, compact operators.

4. Spectral Analysis in Hilbert Spaces: Bilinear and quadratic forms, symmetric operators, normal and self-adjoint operators, the spectral theorem for bounded self-adjoint operators, unbounded self-adjoint operators.

5. Nonlinear Compact Operators and Monotonicity: Banach Fixed point theorem with applications, Schauder fixed point theorem, Frechet derivative, Newton’s method for nonlinear operators, positive and monotone operators.

Office Hours for Theory Course:

Sunday : 1:00 PM - 2 : 00 PM

Tuesday : 11:00 AM - 12 : 00 PM

Wednesday : 2:00 PM - 3 : 00 PM

/ or by appointment.

Important dates:

First (1st) Incourse Date: April 06, 2017. Time 1.30 PM to 2.30 PM

Second (2nd) Incourse Date: May 21, 2017. Time 1.30 PM to 2.30 PM

Office Hours: WEDNESDAY 12pm to 1PM / or by appointment.

Reference Books:

1. A.E. Taylor- Introduction to Functional analysis, John Wiley & Sons, Inc., 1967.

2. V. Hutson and J.S. Pym- Applications of Functional Analysis and Operator theory, Academic press, 1980.

3. W. Rudin- Functional Analysis, McGraw-Hill, Inc. International, 1991.

4. N. Dunford and J Schwartz. Linear operators, General Theory. Wiley, 1958.

Results of assignments and tests are in the following attachment. (please report any errors to hkdas_math@du.ac.bd )

Last Date of Contract: 29/05/2017 before 11 AM.