FUNCTIONAL ANALYSIS

M391C   # 53530  SPRING 1999  Tues-Thurs 9:30-11:00

Instructor: Charles Radin

This is a new second year graduate course, which we expect to offer on
a regular basis - every year or two. We will be using the text
``Essential results of functional analysis'', by R. Zimmer (an
inexpensive paperback), which assumes some knowledge of integration
and basic functional analysis. (The book expects the reader to be
comfortable with the construction and basic properties of L^p spaces,
in particular the Hilbert space structure of L^2. The first semester
of graduate Real Analysis or Applied Math would suffice.) Topics
I hope to cover are: Topological vector spaces (including operator
topologies), convexity and fixed point theorems (including existence
of Haar measure), compact operators (including the Peter-Weyl
theorem), spectral theory (including Stone's theorem on unitary
representations of R^n), Fourier transform and Sobolev embedding,
and distributions (including regularity of elliptic operators).

Consent of instructor will not be required.