MATH 8356 - Functional Analysis II

Credit Hours: (3)

Description The topics covered by the course generally depend on the the instructor as well as educational needs of the students body taking the class. However, some basic topics such as bounded and unbounded operators in Hilbert and Banach spaces, spectral representation and spectral theory for bounded, unitary, selfad- joint, positive, compact operators, Hilbert-Schmidt operators, will be included. Among more specialised topics , an advanced theory of Banach spaces, Sc hauder bases, isometric/ isomorphic structures of Banach spaces, Lp(ν), 1 ≤ p < ∞ , C(K) spaces, Orlicz and Sobolev based spaces will be included.

Applications of Banach space theory to approximation and /or probability theory, and/or PDE, ODE and/or ergodic theory will be presented. A particular choice may depend on the interests of the students. Other more advanced topics will also be considered.

The course (MATH 8356) may be repeated [with a different content] up to 6 credit hours. PREREQUISITE(S)- MATH 8355 or instructor’s permission. Repeatable up to 6 hours PREREQUISITE(S): MATH 8355 Standard Letter