Michael Kiessling
The course 502 is a continuation of Fall’s 501, but also offers outlook on applications in other fields of mathematics, and in mathematical physics and engineering. 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 502 is no longer a mandatory course (it used to be) there is also some flexibility as to the material, thus we may also look into some selected material of sections 10 (Probability theory) and 11 (Haar measure, Hausdorf measure) at the end of the course. I plan to occasionally supplement Folland’s book by “hand outs” of typed-up material. Given the pandemic situation, the course is currently planned to be taught in synchronous remote mode; a room in Hill Center has been booked for in-class instruction in case the situation improves significantly.
Real Analysis, by Folland
501