MA 321: Analysis III
Credits: 3:0
Theory of Distributions: Introduction, Topology of test functions, Convolutions, Schwartz Space, Tempered distributions.
Fourier transform and Sobolev-spaces:Definitions, Extension operators, Continuum and Compact imbeddings, Trace results.
Elliptic boundary value problems: Variational formulation, Weak solutions, Maximum Principle, Regularity results.
Suggested books and references:
- Barros-Nato, An Introduction to the Theory of Distributions, Marcel Dekker Inc., New York, 1873.
- Kesavan, S., Topics in Functional Analysis and Applications, Wiley Eastern Ltd., 1989.
- Evans, L. C., Partial Differential Equations, Univ. of California, Berkeley, 1998.
- Schwartz, L. Hermann, Theorie des Distributions, 1966.