Michael Kiessling
The course 502 is a continuation of Fall’s 501, but also offers an outlook on applications in mathematical physics. We will pick up where the course 501 ended, so 501 is a pre-requisite. The material is mostly from Folland’s book. We begin with some selected material from section 3 (Signed measures and differentiation), then hop to section 5 (Elements of functional analysis) and continue with sections 6 (L p spaces), 7 (Radon measures), 8 (Elements of Fourier analysis) and 9 (Elements of distribution theory). Since the material of 502 is no longer tested on the written qualifying exam, we have some liberty to substitute some of the above by some selected material of sections 10 (Probability theory) or 11 (Haar measure, Hausdorf measure), depending on the preferences of the class. I plan to occasionally supplement Folland’s book by “hand outs†of some functional analysis material that I have typed-up.
"Real Analysis'' by Folland, 2nd ed.
640 501 or equivalent