Pure Math 950 — Fall 2017 — H^p Spaces

Meeting Time: Tuesday and Thursday 10:00 -- 11:30 in MC 5403

Course Outline

• Harmonic functions, Fourier series and Fatou's theorem.
• H^p spaces
• Inner and outer functions
• The disk algebra
• H^\infty and the corona theorem
• Interpolating sequences for H^\infty

Required Background

• complex analysis (essential)
• measure theory (essential)
• functional analysis (some needed, can take concurrently)
• Fourier analysis (helpful, but not necessary)

Grading

• Problem Sets        70
• Talk and paper      30
• No exam

Reference Texts

• Banach spaces of analytic functions by Kenneth Hoffman
• Bounded analytic functions by John Garnett
• Introduction to H_p spaces by Paul Koosis
• Theory of H^p spaces by Peter Duren

Assignments

• Assignment 1 ( the LaTeX code )
• Assignment 2 ( the LaTeX code )
• Assignment 3 ( the LaTeX code )

Talks

Possible topics. Talks will be 40 minutes, and a paper of about 5-10 pages with the details is also required.
You are expected to attend all talks. Talks are all in MC 5403.


Tuesday Dec. 5, 10:00--10:40    Nicholas Manor
                                The Beurling--Lax--Halmos Theorem.


Tuesday Dec.12, 10:00--10:40    Aasaimani Thamizhazhagan
                                Analytic discs in the maximal ideal space of H^\infty.

Tuesday Dec.12, 10:45--11:25    Dan Ursu
                                Taylor coefficients of H^p functions.


Wednesday Dec.13,10:00--10:40   John Sawatzky
                                Extreme points of the balls of H^1 and H^\infty.

Wednesday Dec.13,10:45--11:25   Adam Humeniuk
                                The maximal ideal space and invertibility in H^\infty + C.


Thursday Dec.14, 10:00--10:40   Daniel Pepper
                                Isometries of H^\infty and H^1.




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