The Hardy space is a famous model for the Hilbert space l_2 as holomorphic functions on the unit disk. It was introduced by Hardy almost 100 years ago. Since then, this space and its operators have attracted the attention of many mathematicians, because of the beautiful intertwining of complex analysis and functional analysis one encounters here, and also because of the applications that the theory has in engineering. In this course, we will concentrate on the aesthetic aspect.
By taking this course you will learn more about complex function theory, see some functional analytic operator theory “in action”, and (the lecturer hopes) marvel at the interplay between these two which becomes visible when, e.g., studying invariant subspaces and spectra of so-called Toeplitz and Hankel operators on the Hardy space.
Hours per week
2×45 min lecture.
Exam
Homework assignments. You’ll have ample time between the assignment and the deadline.
Compulsory literature
R.A. Martinez-Avendano and P. Rosenthal: “An Introduction to Operators on the Hardy-Hilbert Space”, ISBN: 978-0-387-35418-7, Springer, 2007 (39.95 euro).
Prerequisites
Basic complex analysis (Analyse 4 is much more than is needed), introduction to functional analysis (Linear Analysis, also in 2007-2008 and 2008-2009, is sufficient), measure theory (Maattheorie).
Recommended for
Those with an interest in functional analysis.
Eligible for
Bachelor study, or master track Applied Mathematics
Remarks
If all participants have access tot the Leiden Blackboard environment, then we can use that. Otherwise a link tot the course’s homepage will be provided on the lecturer’s homepage, see below.
Links