Bergman Spaces
We develop the theory of Bergman spaces and associated Bergman kernels. The theory on the disk for weighted Bergman spaces sometimes resembles that of the Hardy spaces, with inner-outer analogue factorization, and a characterization of the invariant subspaces. There is also a geometric connection, with the classical Bergman metric as a prime example. In some instances asymptotic methods apply, such as with exponentially varying weights. We will discuss such methods as well.
Lecturer
Date
3rd March ~ 26th May, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday | 13:30 - 16:55 | Shuangqing | ZOOM 12 | 815 762 8413 | BIMSA |
Prerequisite
Basic complex analysis and functional analysis
Syllabus
- Classical Bergman spaces on the unit disk and other domains, Bergman kernels, and associated geometric concepts.
- Factorisation theory when available, and related topics in operator theory.
- Invariant subspaces and their structure.
- Depending on student interest we can go towards Hilbert spaces of Dirichlet series, or Grunsky operators and related operator symbols.
Reference
Hedenmalm H, Korenblum B, Zhu K. Theory of Bergman spaces[M]. Springer Science & Business Media, 2012.
Audience
Graduate
Video Public
Yes
Notes Public
Yes
Lecturer Intro
Hedenmalm has mainly contributed to the development of the theory of Bergman spaces and the associated reproducing kernels in one complex variable. In 1996 he became a professor at Lund University and in 1997 he was elected to KFS, the Royal Physiographic Society in Lund. Later, in 2018, he was elected to DKNVS, the Royal Norwegian Society of Sciences and Letters in Trondheim. Hedenmalm has collaborated with a number of other mathematicians, in particular with Alexander Borichev, Serguei Shimorin and Nikolai Makarov. Since 2002 he is professor at the Royal Institute of Technology (KTH) in Stockholm. He received the Wallenberg Prize in 1992, and in 1996 he was invited speaker at 2ECM (second European Congress of Mathematicians) in Budapest. In 2000 he received the Göran Gustafsson Prize (KVA). In 2015, he received the Eva and Lars Gårding Prize from KFS, the Royal Physiographic Society in Lund.