Analysis III

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.

Books

• Barros-Nato, J, : An introduction to the theory of Distributions, Marccl Dekker Inc., New York, 1973.
• Kesavan, S., Topics in Functional Analysis and Applications, Wiley Eastern Ltd., 1989.
• Evans, L. C., Partial Differential Equations, Univ. of California, Berkely, 1998.
• Schwartz, L., Theorice des Distributions, Hermann, 1966.