MATH 712 – Notes

Supplementary Notes

I will post additional notes or information on this page as the semester progresses. Class exercise handouts will be kept at the top of the page. Web links could also be posted here, so let me know if you find something that you think would be useful or interesting to your classmates. If I agree, I will post it.

Class Exercise Handouts

(04/19) Supports and Transforms of Distributions
(04/19) Finite Parts of Integrals
(04/19) Distribution Derivatives of BV Functions
(03/01) Introduction to Fourier Transforms
(03/01) Seminorms and Topologies
(02/25) Nets and Convergence
(02/25) Positive Linear Functionals
(02/02) Introduction to Distributions
(01/26) Weak Derivatives in One Dimension

04/26
  1. Here is a set of notes on primitives of distributions, including elementary
    vector calculus with distributions.
03/03
  1. Here is a set of notes
    on the Fourier transform and Schwartz functions    . All of this material is in Chapter 8
    of Folland, but you might find this presentation to be somewhat less abstract.
03/03
  1. Here is a solution to Folland’s Exercise 7.17.
02/25
  1. The most common approach to the Principle of Uniform Boundedness
    these days proves it as a consequence of the Baire Category Theorem.
    Here is an older proof that, to me at least, is more intuitive.