Hardy spaces on multiply-connected domains and their applications to spectral theory

Seminar: 
Analysis
Event time: 
September 20, 2018 - 4:15pm
Location: 
LOM 215
Speaker: 
Tom VandenBoom
Speaker affiliation: 
Yale
Event description: 

The spectrum of an operator on Hilbert space is a closed subset of the complex plane.  On the spectral complement, there is a family of analytic functions, called resolvent functions, associated to the operator.  A natural inverse question follows: given a closed subset of the plane and a resolvent-type function on its complement, to what extent can we recover the associated operator? This question leads naturally to the study of Hardy spaces on multiply-connected domains.  In this talk, we survey some results applying this perspective to Schroedinger and related operators.