| Date | Speaker | Topic |
|---|---|---|
| Dec. 8 last fall meeting |
Drew Cousino |
Application of Jensen's formula. Factorization into a product of inner and outer functions (Chapter 4): Drew will continue our discussion of Blaschke products, starting with the boundary values of a Blaschke product. He will also introduce us to Hp and discuss how Blaschke products can help us in studying functions analytic in the unit disk. (Sections A and B). |
| Dec. 1 | Genevra Neumann, Drew Cousino |
Elementary boundary behavior theory for analytic functions (Chapter 3):
Genevra will conclude our introduction to
H1 functions in the unit disk
(Section C)
with two applications.
Application of Jensen's formula. Factorization into a product of inner and outer functions (Chapter 4): What's a Blaschke product? When does it converge? What can we say about its boundary values? Why are Blaschke products helpful in studying functions analytic in the unit disk? (Sections A and B). Drew will introduce us to these topics. |
| Nov. 17 | Genevra Neumann | Theorem of the brothers Riesz. Introduction to the space
H1 (Chapter 2):
We will define H1 and
apply what we've learned so far
to deduce some basic properties of H1
(Section B).
Elementary boundary behavior theory for analytic functions (Chapter 3): We will see that H1 functions have non-tangential boundary values ae and will start discussing a uniqueness result for H1 functions. (Sections A, B, and maybe C). |
| Nov. 10 | Chuck Moore, Bob Burckel |
Functions harmonic in the unit disk (Chapter 1):
Chuck Moore will conclude
his discussion of the harmonic conjugate
(section E) and give a brief introduction to singular integrals. Theorem of the brothers Riesz. Introduction to the space H_1 (Chapter 2): Bob Burckel will discuss the F. and M. Riesz theorem (following Bernt K. Øksendal, "A short proof of the F. and M. Riesz theorem", Proc. Amer. Math. Soc. 30 (1971), 204). |
| Nov. 3 | Chuck Moore | Functions harmonic in the unit disk (Chapter 1): Chuck Moore will continue his discussion of the harmonic conjugate (section E). |
| Oct. 27 | Xiang Fang, Chuck Moore |
Functions harmonic in the unit disk (Chapter 1):
Xiang Fang will conclude our discussion of boundary behavior
(section D.3). Chuck Moore will start discussing the harmonic conjugate; i.e., given u(z) harmonic in the unit disk, can we find v(z) harmonic in the unit disk such that f(z) = u(z) + iv(z) is analytic in the unit disk? (section E) |
| Oct. 20 | Xiang Fang | Functions harmonic in the unit disk (Chapter 1): Xiang Fang will continue our discussion of boundary behavior, discussing non-tangential limits and Fatou's theorem (section D.3). |
| Oct. 13 | No meeting | Please go to the colloquium at 2:30 in CW 122 (L. Grafakos: "The disc multiplier, recent results and new challenges") and to the Prairie Analysis Seminar on Oct. 14 and 15. |
| Oct. 6 | Olena Ostapyuk, Dmitry Ryabogin |
Functions harmonic in the unit disk (Chapter 1):
What happens if we start with a function (or a measure)
defined on the unit circle?
Olena will conclude her discussion of sections D.1 and D.2. We've been studying some very technical proofs and it's easy to forget the big picture. What are harmonic functions? Dmitry Ryabogin will give a short introduction to minimal surfaces and the Dirichlet equation. |
| Sept. 29 | Olena Ostapyuk | Functions harmonic in the unit disk (Chapter 1): What happens if we start with a function (or a measure) defined on the unit circle? Olena will continue her discussion of sections D.1 and D.2. | Sept. 22 | Sapto Indratno, Olena Ostapyuk |
Functions harmonic in the unit disk (Chapter 1): What happens if we start with a function (or a measure) defined on the unit circle? Olena will start sections D.1 and D.2. Also, Sapto will finish section C. |
| Sept. 15 | Sapto Indratno | Functions harmonic in the unit disk (Chapter 1): Can we represent a function harmonic in the unit disk as an integral of a function (or a measure) defined on the unit circle? Sapto covered the three theorems in section C. |
| Sept. 8 | Sapto Indratno | Functions harmonic in the unit disk (Chapter 1): Harmonic functions, Poisson's formula, and a start on representing a function harmonic in the unit disk as an integral. (Ch. 1.A - C in Koosis) |
| Sept. 1 | Bob Burckel | Overview. |