Professor David Blecher
Topics course in Analysis:
Analytic Functions, Hardy Spaces and Operator Function Theory (Math 6395)
Time and place : MWF 12-1pm in AH 2
Office Hours MW: 2-3 pm (or by
appointment--email or call 713-743-3451)
Email: dblecher@math.uh.edu
Final exam: Date to be announced.
Prerequisites:
Graduate Standing or consent of instructor.
Some parts of the Real Variables sequence would be helpful, e.g. Math 6320,
and Math 4331-4332 or equivalent. A little topology
and metric spaces, and some basic knowledge of Banach spaces,
particularly Hilbert spaces,
would also be helpful.
Texts/Recommended reading: Banach Spaces of Analytic Functions (Dover Books on Mathematics), by Kenneth Hoffman; ISBN: 978-0486458748. Instructor will also provide some typed notes, drawn from several texts, e.g. Hoffman's book and
Rudin's Real and Complex analysis.
Course description:
This may change slightly based on the makeup of the class. We will start with some important theorems in complex analysis related to normal families of analytic functions. We then will study the basic theory of the disk algebra and the important theory of Hardy spaces (which have not been taught at UH for some years). We will follow Hoffman's book closely here. In the second half of the course we will discuss some operator function theory e.g. related to the invariant subspace problem (Beurling's theorem and generalizations). We will also discuss abstract operator algebras on a Hilbert space and their theory, and connections to noncommutative function theory. The course will end with a choice of student projects depending on what they are each interested in, for example a treatment of noncommutative integration and noncommutative Hardy spaces.
Final grade is aproximately based on a total score
of 300 points consisting of homework (100 points), a semester test
(100 points), and a project/final exam (100 points). Some of these may be
take-home tests.
The instructor may change this at his discretion.
Please send me an email (or give me your email address)
so that you can get the regular course emailings.
Almost all course communication and instructions, assignments, keys
etc. will be sent by email.