Theorems of Phragmén-Lindelöf and an applicationOberseminar Global Analysis and Operator Algebras

by Anton Gleue (Uni Bonn)

Tuesday Jul 14, 2026, 2:15 PM → 3:45 PM Europe/Berlin

Endenicher Allee 60/1-008 (Mathezentrum)

The well known maximum modulus principle tells us that holomorphic functions take
their maximum on the boundary of bounded domains. Theorems of
Phragmén-Lindelöf-type generalise this to types of unbounded domains at the
imposition of some growth condition in the domain's interior. On vertical strips,
this bound can be made more precise: showing logarithmic convexity with respect to
the values on the strip's boundary. This result serves as the basis for the
so-called method of complex interpolation, a general way of constructing
intermediate spaces between two Banach-spaces.